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Whenever horses a, b, c race together, their respective probabilities of winning the race are 0.3, 0.5, and 0.2, respectively. If they race three times, the probability that the same horse wins all the three races, and the probability that a, b, c each wins one race are, respectively

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8/50, 9/50

16/100, 3/100

12/50, 15/50

10/50, 8/50

answer is A.

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Detailed Solution

$P (a) = 0 .3, P (b) = 0 .5, P (c) = 0 .2$ . Hence, a, b, c ate exhaustive.

P(same horse wins all the three races)

= P(aaa or bbb or ccc)

$\begin{array}{l} = (0 .3)^{3} + (0 .5)^{3} + (0 .2)^{3} \\ = \frac{27 + 125 + 8}{1000} = \frac{160}{1000} = \frac{4}{25} \end{array}$

P(each horse wins exactly one race)

= P(abc or acb or bca or bac or cab or cba)

$= 0 .3 \times 0 .5 \times 0 .2 \times 6 = 0 .18 = \frac{9}{50}$

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