What is the expected number of greengreen balls in the​ sample

Question

Suppose three balls are drawn (with replacement) from a bag that contains 4 red balls and 6 green balls. The number of green balls is counted. What is the expected number of greengreen balls in the sample

Answer 1

This is a binomial problem with n =3 and p = .6

 

The expected value of a binomial random variable is np

 

In this case 3(.6) = 1.8

Answer 2

Total number of balls = (4 red + 6 green)

                               = 10 balls

 

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events:

 

So, the expected number of green balls in the sample:

(6/10)*(5/9)= 2/6 = 1/3