`5` players of equal strength play one each with each other. `P(A)=` probability that at least one player wins all matches he (they) play. `P(B)=` probability that at least one player losses all his (their) matches.

Options

A. `P(A)=(5)/(16)`
B. `P(B)=(7)/(16)`
C. `P(AnnB)=(5)/(32)`
D. `P(AuuB)=(15)/(32)`

Answer

A, B, D

Explanation

`(a,b,d)` `P(A)=("^(5)C_(1)2^(6))/(2^(10))=(5)/(16)`, `P(B)=('^(5)C_(1)2^(6))/(2^(10))=(5)/(16)`
`P(AnnB)=("^(5)C_(2)xx2xx2^(3))/(2^(10))=(5)/(32)`
`implies P(AuuB)=(15)/(32)`