Question

A bag contains $10$ red balls and $8$ green balls. $2$ balls are drawn at random one by one with replacement. Find the probability that both the balls are green that a second year student is chosen.

Answer 1

In a conditional probability, if $A$ and $B$ are independent events, then $P(A\cap B)=P\left(A\right)P\left(B\right)$

Given$:$Total number of red balls$=10$ and that of green balls$=8$

Probability of drawing a red ball$=\frac{10}{18}=\frac{5}{9}$

Probability of drawing a green ball$=\frac{8}{18}=\frac{8}{9}$

Probability of both the balls are green $=P$(a green is drawn first and green is drawn second time also )

$=P$(drawing a green)$\times P$(drawing a green)

$=\frac{4}{9}\times \frac{4}{9}=\frac{16}{81}$