- Home
- Standard 11
- Mathematics
A box $'A'$ contanis $2$ white, $3$ red and $2$ black balls. Another box $'B'$ contains $4$ white, $2$ red and $3$ black balls. If two balls are drawn at random, without replacement, from a randomly selected box and one ball turns out to be white while the other ball turns out to be red, then the probability that both balls are drawn from box $'B'$ is
$\frac{7}{{16}}$
$\frac{9}{{32}}$
$\frac{7}{{8}}$
$\frac{9}{{16}}$
Solution
Probability of drawing a whiteball and then a red ball from bag $B$ is given by
$\,\frac{{^4{C_1} \times {\,^2}{C_1}}}{{{\,^9}{C_{ 2}}}} = \frac{2}{9}$
Probability of drawing a whiteball and then a red ball frombag $A$ is given by
$\,\frac{{^2{C_1} \times {\,^3}{C_1}}}{{{\,^7}{C_{ 2}}}} = \frac{2}{7}$
Hence, the probability of drawing a white ball and then a red ball from bag $B$
$=\frac{\frac{2}{9}}{\frac{2}{7}+\frac{2}{9}}=\frac{2 \times 7}{18+14}=\frac{7}{16}$
