Question

A box contains 20 black balls and 80 white ones. One hundred balls are drawn at random with replacement.

Find the expected number of black ball among the draws.

Answer 1

Solution:

20 Black balls + 80 White balls = Total 100 balls.

Probability of " randomly selected ball is black" is 20/100 = 0.2

Say p = 0.2

Now , One hundred balls are drawn at random with replacement.

With replacement , so it goes to Binomial distribution.

Number of trials = n = 100

X be the number of black ball among the draws.

X follows Binomial(n = 100 , p = 0.2)

Using Binomial properties,

E(X) = n * p = 100 * 0.2 = 20

Answer : expected number of black ball among the draws is 20