Question

In a region there is a 0.95 probability chance that a randomly selected person of the population has brown eyes. Assume 15 people are randomly selected. Perform the following:
a) Find the probability that all of the selected people have brown eyes.
b) Find the probability that exactly 14 of the selected people have brown eyes.
c) Find the probability that the number of selected people that have brown eyes is 13 or more.

Answer 1

We are given the data of  0.95 probability chance that a randomly selected person with brown eyes. 
we use the formula: nCm* p^m q^ (n-m)
a) 15C15* 0.95^15* 0.05^ (0) = 0.463
b) 15C14* 0.95^14* 0.05^ (1) = 0.366
c) 15C13* 0.95^13* 0.05^ (2) = 0.135
    0.135+0.366+0.463= 0.964