







(x+y)^n = x^n + y^n + Z 
20040318 

JeanSébastien pose la question : Bonjour,
je me m’appelle
JeanSébastien et je suis étudiant en secondaire
4. Je me demandais s’il est possible de développer le terme
(x+y)^{n}, lorsque n est un entier positif. Il est évident
que x^{n}+y^{n} fera partie de la réponse mais comment définir le reste (Z
dans l’exemple cidessous)?
(x+y)^{2} = x^{2}+y^{2}+2xy
(x+y)^{n} = x^{n}+y^{n}+ Z
P.S. : Une preuve mathématique démontrant la possibilité ou
l’impossibilité du problème serait grandement appréciée,
merci. Claude Tardif lui répond. 





nC0 + nC1 + nC2 + .... + nCn = 2^n 
20180219 

bristal pose la question : (QQ) Prove, nC0 + nC1 + nC2 + .... + nCn = 2^n. Penny Nom lui répond. 





Expand and simplify [x3][x+3] 
20140716 

symion pose la question : Expand and simplify [x3][x+3] Penny Nom lui répond. 





Identify each polynomial by its degree and number of terms 
20110110 

betty pose la question : Write in standard form and identify each polynomial by its degree and number of terms. How do you do this? Penny Nom lui répond. 





A binomial random variable 
20101129 

yvette pose la question : a binomial random variable has a mean equal to 200 and standard deviation of 10. find the values of n and p. Penny Nom lui répond. 





(x + a)^2 
20100604 

a pose la question : If the 3rd , 4th, 5th terms in the expansion of (x + a)powe "n" are 720, 1080, 810 respectively, then
find the values of x, a and n. Penny Nom lui répond. 





Sample size 
20100329 

Rae pose la question : What sample size was needed to obtain an error range of 2% if the following statement was made? "75% of the workers support the proposed benefit package. These results are considered accurate to within + or  2%, 18 out of 20 times. This seems like a straight forward question but I'm getting it wrong. Could you please help me out even just the set up would be appreciated so I can see if that's where I'm going wrong. Thanks Harley Weston lui répond. 





Binomial probability 
20100319 

Rana pose la question : According to one study, it has been claimed that 65% of all single men in Montreal would welcome a
woman taking the initiative in asking for a date. You decide to challenge this study by performing a little
experiment of your own. You randomly select 15 single men from around Montreal and ask them if they
would be comfortable with a woman asking them out for a date. If the claim made by the study was
true, what is the probability that:
a) Exactly 9 men would say yes?
b) Exactly 6 men would say no?
c) More than 11 men would say yes?
d) At most 4 men would say no? Penny Nom lui répond. 





0.999 ^ (500) 
20100307 

debra pose la question : I just need to know how to solve the following problem without using a calculator: .999 ^ (500). I know the answer is .606, I just want to do it by hand since I can't use a calculator on my test. Penny Nom and Claude Tardif lui répond. 





The binomial distribution 
20100227 

Jessica pose la question : A small mobile phone retailer has found that one of their phones has a 12% probability of being faulty and a replacement having to be provided for the customer. They have just
received a trial order for 10 phones from their biggest customer who will take their business elsewhere if 20% or more items are faulty.
i) what is the probability that they will lose their biggest customer? Penny Nom lui répond. 





The binomial theorem 
20100121 

Laura pose la question : Using the fact that (1 + x)^4 * (1 + x)^9 = (1 + x)^13 show (4C0 * 9C4 + 4C1*9C3 + 4C2*9C2 + 4C3*9C1 + 4C4*9C0) = 13C4 Harley Weston lui répond. 





nC0 + nC1 + nC2 + ... + nCn = 2^n 
20090615 

Chinonyerem pose la question : For n >= 1, derive the identity
nC0 + nC1 + nC2 + ... + nCn = 2^n
[Hint: Let a = b = 1 in the binomial theorem] Penny Nom lui répond. 





A multiple choice exam 
20080913 

Phalange pose la question : A multiple choice exam consists of 12 questions, each having 5 possible answers. To pass, you must answer at least 9 out of 12 questions correctly. What is the probability of passing if:
a. You go into the exam without knowing a thing, and have to resort to pure guessing?
b. You have studied enough so that on each question, 3 choices can be eliminated. But then you have to make a pure guess between the remaining 2 choices.
c. You have studied enough so that you know for sure the correct answer on 2 questions. For the remaining 10 questions you have to resort to pure guessing. Harley Weston lui répond. 





n choose r equals n1 choose r plus n1 choose r  1 
20080714 

fae pose la question : Prove that
( n ) = ( n – 1) + ( n  1 )
( r ) ( r ) (r1)
NOTE: the ( ) should be one for n taken r and so on. but there is no one big ( ) that will cater two lines Janice Cotcher lui répond. 





A coin is tossed 30 times 
20080413 

seulki pose la question : coin tossed 30 times, what is the probability that the heads show up fewer than 17 times? Harley Weston lui répond. 





Probability and Merta trains 
20080327 

Lorie pose la question : 4. Merta claims that 74% of its trains are on time.
a. Find the probability that among the 60 trains, 38 or fewer arrived on time. Harley Weston lui répond. 





Multiple guess 
20080227 

debbie pose la question : What is the probability of getting 6 out of 10 (a,b,c,d,e) questions correct, by random selection? Stephen La Rocque lui répond. 





A binomial probability problem 
20080108 

rougi pose la question : According to statistics of the company about 4% of the people who buy tickets do not arrive to the flight . The company sells 205 tickets to plane that has 200 places . Use the binomial distribution to calculate what is the probability that all the people who come to the flight get a place. Harley Weston lui répond. 





Binomial probability 
20071110 

areej pose la question : In any table of binomial probability with n trials, why is it that the probabilities for k=n are not tabulated??? Harley Weston lui répond. 





A multiple choice exam 
20071021 

jon pose la question : a student is taking a multiple choice exam in which each question has four choices.
assuming that she has no knowledge of the correct answers to any of the questions, she
has decided on a strategy in which she will place four balls (marked A, B, C, D) into a box. she randomly
selects one ball for each question and replaced the ball in the box. the marking will determine her answer to the question.
there are five multiple choice questions on the exam. what's the probability that she will ... Stephen La Rocque and Harley Weston lui répond. 





The normal approximation to the binomial 
20070930 

m.j. pose la question : Slot Machines The probability of winning on a slot machine is 5%. If a person plays the machine 500 times, find the probability of winning 30 times. Use the normal approximation to the binomial distribution. Harley Weston lui répond. 





Standard deviation 
20070901 

Pat pose la question : I have looked over your math question and mines is not there. for a binomiial distribution with parmeter n and p, the mean is np and the standard deviation is np(1p). I understand how to get the np but not understanding how to get the (1p). For example np=(40)(0.48)(10.48)=3.160. How can I get the (10.48) answer please Harley Weston lui répond. 





Find the sample size needed 
20070513 

Mini pose la question : Find the sample size needed to be 98% confident thata marketing survey on the proportion of shoppers who use the internet for holiday shopping is accurate within a margin of error of 0.02. Assume that the conditions for a binomial distribution are met, and that a current estimate for a sample proportion does not exist. Penny Nom lui répond. 





the sum form r = 0 to r = m of C(n+r,n)=? 
20070415 

Aastha pose la question : FIND THE VALUE OF:
the sum form r = 0 to r = m of C(n+r,n)=? Penny Nom lui répond. 





A hypothesis test 
20070409 

Katrina pose la question : I have already tried to do this problem but im having a very had time with
it. Can you please help me.
Glamour Magazine sponsored a survey of 2500 prospective brides and
found that 60% of them spent less than $750 on their wedding gown.
Use a 0.01 significance level to test the claim that less than 62% of brides
spend less than $750 on their wedding gown. How are the results
affected if it is learned that the responses were obtained from magazine
readers who decided to respond to the survey through an Internet Web
site? Penny Nom lui répond. 





Colour blindness 
20070329 

Katrina pose la question : 9% of men and .25% of woman can't distinguish between
the colors red and green. This is the type of color blindness
that causes problems with traffic lights. If 6 men are randomly
selected for a study of traffic signal perceptions, find the probability
that exactly two of them cannot distinguish between red and green. Stephen La Rocque lui répond. 





Acceptance sampling 
20070329 

Katrina pose la question : The Medassist Pharmaceutical Company recieves large shipments of
asprin tablets and uses this acceptance sampling plan: Randomly select
and test 24 tablets, then accept the whole batch if there is only one or
none that doesnt meet the required specifications. If a particular shipment
of thousands of asprin tablets actually has a 4% rate of defects, what is
the probability that this whole shipment will be accepted? Penny Nom lui répond. 





What is the expected number of ripe and ready to eat watermelons 
20061129 

James pose la question : An agricultural cooperative claims 95 percent of the watermelons shipped out are ripe and ready to eat. If 20 watermelons are shipped out , what is the probability that the number of watermelon that are ripe and ready to is (i) exactly 14 (ii) more than 18 (iii) of the 20 watermelons that are shipped what is the expected number of ripe and ready to eat watermelons Penny Nom lui répond. 





Sally plays roulette 
20061121 

Sherry pose la question : Sally plans to bet 100 bets of $1.00 each on red roulette. the probability of the ball landing on red is 18/38 what is the probability that Sally will win at least half the time Penny Nom lui répond. 





Prove that 2nCn is less than 4n, for all positive integers n? 
20061001 

Anna pose la question : How can I prove that 2nCn is less than 4n, for all positive integers n? Penny Nom lui répond. 





Square roots in a binomial expansion 
20060911 

Sydney pose la question : (√x + 5)^{4} expanded using the binomial theorem Penny Nom lui répond. 





What are the 3rd and 4th terms of (2xy)^7? 
20060618 

April pose la question : What are the 3rd and 4th terms of this sequence: (2xy)^{7}?
I'm having an issue with this...is there any easier way to get it without completely factoring the whoooole thing out? Penny Nom lui répond. 





The coefficient of variation 
20060520 

Glenn pose la question : What is the correct formula for coefficient of variation for a binomial distribution? Penny Nom lui répond. 





A manufacturer of cotton pins 
20060320 

Nirmal pose la question : A manufacturer of cotton pins knows that 5% of his products are defective. If he sells cotton pins in boxes of 100 and guarantees that not more than 10 pins will be defective, what is the approximate probability that a box will have the guaranteed quantity? Penny Nom lui répond. 





A binomial distribution exercise 
20060121 

Belinda pose la question : In a survey of 15 manufacturing firms, the number of firms that use LIFO (a lastin firstout accounting procedure for inventory) is a binomial random variable x with n=15 and p=0.2.
a) What is the probability that five or fewer firms will be found to use LIFO? Is it unlikely that more than 10 firms will be found to use LIFO? Comment. Penny Nom lui répond. 





A confidence interval 
20060121 

Jonathan pose la question :
I am attempting to calculate how my confidence interval will widen at the 95% confidence level if my response universe increases from 100 to 150 or to 200.
There is a universe of 54,000. I take a 5% sample for a test universe of 2,700
If my "yes" universe is 100, at the 95% confidence level, what is my +/ range? (i.e +/ 3? +/5?)
Historically, 6.6% of the 2,700 you say "yes". I am trying to determine how the confidence interval would change if the number of "yes" responders increased to 150 or to 200.
Penny Nom lui répond. 





5x^2  27x  18 
20060113 

Katy pose la question : How would you factor 5x^{2}  27x  18? Penny Nom lui répond. 





A sample size estimation 
20051203 

Ivonne pose la question : I have to do a research about the behavior of library users. We are going to apply a survey to a population of 1280 students (Management an Economics students) but of course we have to do it to a sample....I need to know the size of my sample. Penny Nom lui répond. 





Discrimination based on gender? 
20050310 

A student pose la question : After being rejected for employment, Kim learns that the Bellevue office has hired only two women among the last 20 new employees. She also learns that the pool of applicants is very large, with an approximately equal number of qualified men and women. Help her address the charge of gender discrimination by finding he probability of getting two or few women when 20 people are hired, assuming that there is no discrimination based on gender. Does the resulting probability really support such a charge? Penny Nom lui répond. 





Computing confidence intervals 
20041126 

Christie pose la question : I was given a question with N=100, sample proportion is 0.1 compute the 95% confidence interval for P? I have tried this several ways but do not know how to do without means, standard deviations, standard error of the mean? I asked my teacher and she said I have all the info I need. Can you help???? Penny Nom lui répond. 





A binomial squared 
20040919 

John pose la question : Can you explain the steps
for me, that get you from (a  b)^{2} to a^{2} 
2ab + b^{2} Penny Nom lui répond. 





Replacement times for TV sets? 
20040331 

Barb pose la question : Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. Estimate the probability that for 250 randomly selected TV sets, at least 15 of them have replacement times greater than 10.0 years.e Andrei Volodin and Penny Nom lui répond. 





Binomial distribution 
20031217 

Lesley pose la question : my daughter is having difficulty with the following formula
P(X=x) = ( n over x) px (1p) nx
The teacher has given them the formula but not taught them how to apply it or understand it. Penny Nom lui répond. 





Newton's binomial theorem 
20030830 

William pose la question : According to page 126 of Murtha & Willard's "Statistics and Calculus" (PrenticeHall, 1973), Newton's binomial theorem can proved inductively. I suppose that was his method, which I would like to see. Penny Nom lui répond. 





A binomial probability 
20030430 

Erica pose la question : In a biathlon, athletes shot at 20 targets. A particular athlete had a probability of 0.18 of missing a target. Assuming a binomial distribution, what is the probability, to the nearest thousandth, that the athlete hit exactly 16 targets? Andrei Volodin lui répond. 





The effectiveness of a drug 
20030422 

A student pose la question : A certain drug is found to be effective 80% of the time. Find the probability of successful treatment in two out of four cases. Andrei Volodin lui répond. 





Successive coefficients in Pascal's Triangle 
20021227 

Quincy pose la question : There is a formula connecting any (k+1) successive coefficients in the nth row of the Pascal Triangle with a coefficient in the (n+k)th row. Find this formula Penny Nom and Walter Whiteley lui répond. 





Successive coefficients in the nth row of Pascal's Triangle 
20020610 

Tim pose la question : There is a formula connecting any (k+1) successive coefficients in the nth row of Pascal's Triangle with a coefficient in the (n+k)th row. find this formula. Penny Nom lui répond. 





Pascal's Triangle 
20020402 

Brian pose la question : It's about (a+b)^{x}. I remember there a triangle with numbers to remember for a faster solution. Can you please teach me? Penny Nom lui répond. 





Rolling 5 sevens before rolling a six or an eight 
20020120 

Tony pose la question : When rolling 2 dice, what is the probability of rolling 5 sevens before rolling a six or an eight? Andrei Volodin and Penny Nom lui répond. 





Cinderella clothes 
20011211 

A student pose la question : If cinderella clothes, inc. has determined that 0.5% of all incoming phone calls involve complaints, what is the probability that in 200 incoming calls there are more than one complaint? Andrei Volodin lui répond. 





Multinomial theorem 
20011128 

Murray pose la question : Could you please state and explain the multinomial theorem (I already know the binomial theorem etc, to give you an idea of where i am) Harley Weston lui répond. 





(a+b) squared and a squared plus b squared 
20011114 

Kristen pose la question :
(a+b)^{2} = a^{2} + b^{2} Is this true for all whole numbers, and why? Penny Nom lui répond. 





Lucas' theorem 
20011009 

Tania pose la question : How could I demonstrate: nCp is congruent to floor(n/p) (modulo p)? where rCk is a binomial coefficient, rCk = r(r1)...(rk+1)/k(k1)...1, and p is a prime number Richard McIntosh lui répond. 





Binomial probabilities 
20011008 

Amna pose la question : I had a few binomial probability questions which I can not use from the tables as instructed:  If 60 % of television viewers are watching a certain program, what is the probability tha tmore than half of those selected in a random sample of five will be watching the specified program?
 If it is known according to Mendel's Law, that we can expect in teh long run to have 3 white, 1 brown rabbits in every 4 rabbits of a certain type, what is the probability that 2 in a litter of 3 will be white?
 On the average, 2% of the items sold in a department store are returned for refunds. what is the probability that of its next five items sold, at most two will be returned for refunds?
Leeanne Boehm lui répond. 





Multiplying binomials 
20010908 

A student pose la question : (x+1)(x+2)=? (2x1)(x4)=0 please tell me this question!! Leeanne Boehm lui répond. 





(2b+3)(b1) 
20010206 

Melissa pose la question : Alright, lets say you are multiplying (2b+3)(b1) and you are using "FOIL" first you would get : 2b^{2}+2b3b3 then you add liketerms. when multiplying,if the bases are the same, add the exponents...does the same thing apply when you are adding the results of the multiplication even though it's addition? would the answer be 2b^{3}3b3 or would it be 2b^{2}b3? Penny Nom lui répond. 





A dollar, quarter, dime, nickle and penny 
20010107 

Sarah pose la question : Arnold has a dollar coin, one dime, one quarter, one nickel, and a penny. The number of different sums of money that can be formed using three coins is... Penny Nom lui répond. 





Banana yogurt 
20001103 

James pose la question : A grocery store has 100 cartons of banana yogurt in stock.Each carton contains 12 cup of banana yogurts.The probability that a cup has fewer than 20 banana chunks in it is 10 %. So,What is the probability that between 15 and 25 (inclusive) cartons out of the 100 cartons have exactly 3 cups with fewer than 20 banana chunks? Harley Weston lui répond. 





Independent tests 
20001007 

A student pose la question : If the falsepositive rate of each test in a battery of tests is 0.05, how many independent tests can be included in the battery if we want the probability of obtaining at least one falsepositive result to be at most 0.2? Harley Weston lui répond. 





649 
20000914 

Steve pose la question : In our state lottery you must choose 6 numbers (149). How many different combinations are there? They can be in any order. Harley Weston lui répond. 





An expected value 
20000424 

Carl Pride pose la question : Suppose that in a statistics class of size 23, each student has a probability of passing of 73 percent. sample: What is the expected number of students who will pass?? Harley Weston lui répond. 





Binomial coefficients 
20000321 

Howard Lutz pose la question : How do you find each successive numerical term in this equation y+dy=(x+dx)^{5} =x^{5}+5*x^{4}dx+10*x^{3}(dx)^{2}+10*x^^{2}(dx)^{3}+5*x(dx)^{4}+(dx)^{5} I would appreciate an explanation of the method to find the numeric coefficient in a binomial expansion Penny Nom lui répond. 





Multinomial coefficients 
19991203 

Suraj Das pose la question : Is there a formula for the expansion of (a+b+c) to the nth power? Does it have to do with Pascal's triangle? Penny Nom lui répond. 





The Binomial Theorem for rational exponents 
19990415 

Angela Evans pose la question : The full question is this: Isaac Newton generalized the Binomial Theorem to rational exponents. That is, he derived series of expansions for such expressions as (x+y)^{3} (x+y)^{2/3} (x+y)^{5/6} What did Newton find? What are the first four terms of the series expansions of binomials above? How can this extended Binomial Thrm. be used to aid in calculations? Penny Nom lui répond. 





Factoring 
19990330 

Maggie Stephens pose la question : I don't know anything about factoring would you plese help me. 3x^{4}  48 54x^{6} + 16y^{3} 1258x^{3} 12x^{2}  36x + 27 9  81x^{2} a^{3} + b^{3}c^{3} I would greatly appreciate any help you can give me thanks. Jack LeSage lui répond. 





Cannonballs 
19990127 

Roger King pose la question : How many cannonballs can be stacked in a triangular pyramid? Penny Nom lui répond. 





Three keys 
19981126 

Karen Chan pose la question : A man has a bunch of three keys, only one of which fits the lock of his front door. When he comes home in the dark he tries the keys at random until he finds the one fits. Find the probability that in a week of five nights, he tries the right key first on at least one night. Penny Nom lui répond. 





What's the next term? 
19981112 

Ilia pose la question : What the formula and explonation for formula for next patterns: 1) 1, 4, 10, 20, 35, 56, 84,... 2) 0, 6, 30, 90, 210, 420,... Thanks! Penny Nom lui répond. 





What is the variance of the difference of two binomials? 
19960208 

Chris Johnson pose la question : My coworkers and I have come up with different estimates of the zstatistic, and are in particular disagreement over the calculation of Variance for this problem. I am trying to find out, with a five percent level of significance, whether the new form yields a higher rate of return than the old form. Any thoughts, comments, or solutions? Harley Weston lui répond. 

