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 pr4obability t hat the same horse wins all the three races, and the probability that `a , b ,c` each wins one race are, respectively. `8//50 ,9//50` b. `16//100 ,3//100` c. `12//50 , 15//50` d. `10//50 ,8//50`

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`