A bag contains 8 black and 7 white balls. Two | vedclass

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(B) Total number of balls $= 8 + 7 = 15$.Total ways to draw $2$ balls $= {}^{15}C_2 = \frac{15 	imes 14}{2} = 105$.$1$. Probability that both balls a

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One ball is white and one is black

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(B) Total number of balls $= 8 + 7 = 15$.Total ways to draw $2$ balls $= {}^{15}C_2 = \frac{15 	imes 14}{2} = 105$.$1$. Probability that both balls are white: $P(WW) = \frac{{}^7C_2}{{}^{15}C_2} = \frac{21}{105} = \frac{1}{5} = 0.2$.$2$. Probability that both balls are black: $P(BB) = \frac{{}^8C_2}{{}^{15}C_2} = \frac{28}{105} = \frac{4}{15} \approx 0.266$.$3$. Probability that one ball is white and one is black: $P(WB) = \frac{{}^7C_1 	imes {}^8C_1}{{}^{15}C_2} = \frac{7 	imes 8}{105} = \frac{56}{105} = \frac{8}{15} \approx 0.533$.Comparing the probabilities: $\frac{8}{15} > \frac{4}{15} > \frac{3}{15}$.Thus,the probability of drawing one white and one black ball is the highest.

$A$ bag contains $8$ black and $7$ white balls. Two balls are drawn at random. For which of the following is the probability the highest?

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