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

Options

A. `8//50,9//50`
B. `16//100,3//100`
C. `12//50,15//50`
D. `10//50,8//50`

Answer

A

Explanation

`P(a)=0.3P(b)=0.5,P(c)=0.2.` Hence, a,b c are exhaustive. P(same horse wins all the three reces)
=P(aaa or bbb or ccc)
`=(0.3)^(3)+(0.5)^(3)+(0.2)^(3)`
`=(27=125+8)/(1000)=(160)/(1000)=4/25`
P(each horse wins exactly one race)
=P (abc or cab or bca or bac or cab or cba)
`=0.3xx0.5xx0.2xx6=0.18=9/50`