Question

A box contains 4 blue, 5 green and 4 yellow balls. Two balls are drawn with replacement. Find the probability that the first ball is blue and the second ball is yellow.

• A. $\frac{1}{13}$
• B. $\frac{16}{169}$
• C. $\frac{20}{169}$
• D. $\frac{4}{13}$

Answer 1

The correct option is B $\frac{16}{169}$

Let A be the event that the first ball is blue
and B be the event that the second ball is yellow.
Since balls are drawn with replacement, so the
size of the sample space remains constant.
So the events A and B are independent events.

$ThenP\left(A\cap B\right)=P\left(A\right).P\left(B\right)=\frac{4}{13}\times \frac{4}{13}=\frac{16}{169}.$