Problem 1RE

In Exercises, assume that 40% of the population has brown eyes (based on data from Dr. P. Sorita at Indiana University).

Brown Eyes If six people are randomly selected, find the probability that none of them has brown eyes.

Answer:

Step 1:

Given that, if six people are randomly selected, to find the probability that none of them has brown eyes.

Assume that 40% of the population has brown eyes.

Here, P = 40% = 0.4, q = 1 - p = 1 - 0.4 = 0.6.

Here ‘x’ follows binomial distribution with sample size “n” and proportion “p”.

i.e, X

Probability mass function of binomial distribution is given by

P(x) = , x = 0,1,2,...,n.

Assuming that 40% of the population has brown eyes,the probability that none of the 6 randomly selected persons has brown eyes is given by the binomial probability.

P(0) =

P(0) = 0.047.