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 ______.

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KollegeApply · Accepted Answer

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($\frac{18}{95}$). 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 $\times$ 8 $\times$ |\underline{7}}{|\underline{7}}}{\frac{20 $\times$ 19 $\times$ |\underline{18}}{|\underline{18}}} \end{aligned} = (9 $\times$ 8)/(20 $\times$19) = $\frac{18}{95}$

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