Two balls are drawn at random with replacement from a box contain… - Vidyadip

Question

Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that,

Both balls are red,
First ball is black and second is red,
One of them is black and other is red.

✓

Answer

The Box contains 10 black balls and 8 red balls. Then $\text{P(Black ball)}=\frac{10}{18}$ $\text{P(red ball)}=\frac{8}{18}$

P(Both ballls are red) $=\frac{8}{18}\times\frac{8}{18}=\frac{16}{81}$
P (First ball is black and second is red) $=\frac{10}{18}\times\frac{8}{18}=\frac{20}{81}$
P (One of them is black and other is red)

$=\frac{10}{18}\times\frac{8}{18}+\frac{8}{18}\times\frac{10}{18}$
$=2\Big(\frac{20}{81}\Big)$
$=\frac{40}{81}$

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