How do you use Binomial Distributions?

Question

Whenever Gwen rents a movie from Amazon Prime, the probability that it will be a comedy is 52%. Of the next seven movies that she rents, what is the probability that she rents no more than two comedies?

The chance of winning a certain game at a carnival is 2 in 5. If Andy plays the game 12 times, what is the probability that he loses at most 3 times?

27% of adults in the US say that apple pie is their favorite type of pie. If 15 adults are randomly selected, what is the probability that more than six of them say that their favorite type of pie is an apple pie? 

what is the probability that four to eight of them say that their favorite type of pie is an apple pie? 

Answer 1

Ah.... a three for..... out of the next 10 questions that I answer, what is the chance that I will have to answer no more than two questions in any of the 10 question? Is this also a binomial distribution?

OK, now for the answers you have been waiting for.

A). Binomial distribution, probability of success (comedy) is always p for each trial and each trial is independent of the others. X a random variable representing the number of successes in n trials.

n = 7(movies), p = .52 calculate P(x≤2) = bicdf(7,.52,2) = .1951

B) Probability of loosing = 3/5 or .6. n trials = 12, x is number of losses. P(x≤3) = bicdf(12,.60,3) = .0153 (a loosing proposition)

C1) Random selection of 15 hungry adults with the probability that thy will report apple as their favorite pie being .27. If x is number reporting "apple 3.14159" as their favorite, what is the chance that x is 7 or more?

This is the same as 1 - the chance that x is 6 or less. This is 1 - bicdf(15,.27,6) or .0817

C2). Calculate odd for 8 or less and subtract the odds of 3 or less, and you get the range 4 to 8.

= bicdf(15,.27,8) - bicdf(15,.27,3) = .6013.

Four for the price of one.