Finite Math Question Please Answer!!

Question

The probability that an individual is right-handed is 0.90. In a class of 25 students, find the probability that...

(Let X = number of individuals who are right-handed)

a. 22 students are right-handed

b. at most 23 students are right-handed

Answer 1

Hi Luke. Use the binomial probability theorem as you would for analyzing results of a series of coin tosses. Here the probability of "success" on a single trial is 0.90 and the probability of "fail" on a single trial is 0.10. The sample size is 25. So for part (a), the probability that X = 22 equals the combination 25 things taken 22 at a time times (0.90)^22 times (0.10)^(25-22). For part (b) it seems easier to use the complement of a set. In this case, you would find the binomial probability that X = 24 or X = 25. Then the probability that X is at most 23 is one minus the probability that X = 24 or X = 25.

Robert