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Question

# 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" is p and the probability that a,b,c each wins one race is q, then the value of pq is (Assume no dead heat)

A
98
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B
89
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C
32
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D
23
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Solution

## The correct option is B 89Given: P(a)=0.3 P(b)=0.5 P(c)=0.2 Probability that "the same horse wins all the three races" =(0.3)3+(0.5)3+(0.2)3=271000+1251000+81000=1601000=850=p Now, a,b,c each wins one race ∴ Total ways of happening =3!=6 ways ∴required probability=6×(0.3)(0.5)(0.2) =6×301000=950=q ∴pq=8/509/50=89

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