Question

A ball is drawn from an urn containing 3 white and 3 black balls. After the ball is drawn, it is replaced and another ball is drawn. This process goes on indefinitely. What is the probability that of the first 4 balls drawn, exactly 2 are white?

Answer 1

Answer:0.375

Explanation:

Given

An Urn contains 3 White and 3 black balls

Ball is replaced after it is drawn

Using Binomial Distribution as trials are finite

n=4 i.e. 4 balls are drawn

Probability of getting white ball $(p)=\frac{1}{2}$

Probability of getting a Non-white ball$(q)=\frac{1}{2}$

$P(X=r)= ^nC_r(p)^r(q)^{n-r}$

For Exactly 2 white balls

$P(X=2)=^4C_2(\frac{1}{2})^{2}(\frac{1}{2})^{2}$

$P(X=2)=\frac{4!}{2!\cdot 2!}\times \frac{1}{2^4}$

$P(X=2)=\frac{3}{8}$