Question

A ball is drawn from an urn containing three white and three black balls. After the ball is drawn, it is then replaced and another ball is drawn. This goes on indefinitely. What is the probability that of the first four balls drawn, exactly two are white?

Answer 1

Answer:

The probability is 3/8

Step-by-step explanation:

The urn has 3 White and 3 Black balls

Probability of drawing a white ball $=\frac{3}{6}$ = $\frac{1}{2}$

Thus, probability of drawing a black ball $=1-\frac{1}{2}$$=\frac{1}{2}$

Since the balls are replaced, the probability of drawing the black or white ball at each turn does not changed

Probability that out of 4 exactly 2 balls are white

$={4\choose 2} \times (\frac{1}{2})^2\times(\frac{1}{2})^{4-2}$

$=6\times \frac{1}{4}\times\frac{1}{4}$

$=\frac{3}{8}$

Hope this helps.