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

The probability that of the first 4 balls drawn, exactly 2 are white is 0.375

How to get the probability

Total balls

= 3 white + 3 black

= 6 balls

Probability of white

= 3 / 6

= 0.5

n is sample = 4 balls

This solution would have to follow a binomial distribution such that

⁴C₂ * 0.5² * (1 - 0.5)²

= 6 * 0.25 * 0.25

= 0.375

The probability that of the first 4 balls drawn, exactly 2 are white is 0.375

Answer 2

Answer:0.375

Step-by-step 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)=(1)/(2)`

Probability of getting a Non-white ball
`(q)=(1)/(2)`

`P(X=r)= ^nC_r(p)^r(q)^(n-r)`

For Exactly 2 white balls

`P(X=2)=^4C_2((1)/(2))^(2)((1)/(2))^(2)`

`P(X=2)=(4!)/(2!\cdot 2!)* (1)/(2^4)`

`P(X=2)=(3)/(8)`