Question

A bag contains 9 red, 7 white and 4 black balls. If two balls are drawn at random without replacement, the probability that both balls are red will be ______.

पर्याय

• `11/95`

• `18/95`

• `18/85`

• `18/23`

Answer 1

A bag contains 9 red, 7 white and 4 black balls. If two balls are drawn at random without replacement, the probability that both balls are red will be `bbunderline(18/95)`.

Explanation:

We have, 9 red, 7 white, 4 black balls.

Total balls = 20

Let E be the event that two balls are red.

So, the favourable cores are: ⁹C₂

Total no. of outcomes of drawing 2 balls is ²⁰c₂

\[\begin{aligned}
& \mathrm{P(E)}=\frac{^9\mathrm{C}_2}{^{20}\mathrm{C}_2} \\
& =\frac{\frac{|\underline{9}}{|\underline{2}|\underline{7}}}{\frac{|\underline{20}}{|\underline{2}|\underline{18}}} \\
& =\frac{\frac{9\times8\times|\underline{7}}{|\underline{7}}}{\frac{20\times19\times|\underline{18}}{|\underline{18}}}
\end{aligned}\]

= `(9 × 8)/(20 ×19)`

= `18/95`