A man has 3 pairs of black socks and 2 pair of brown socks kept together in a box. If he dressed hurriedly in the dark, the probability that after he has put on a black sock, he will then put on another black sock is `1//3` b. `2//3` c. `3//5` d. `2//15`

Options

A. `1//3`
B. `2//3`
C. `3//5`
D. `2//15`

Answer

A

Explanation

(1) `P(B_(1))=(""^(6)C_(1))/(""^(10)C_(1))=6/10=3/5`
`P(B_(2)//B_(1))=5/9(B_(2)="black")`
`thereforeP(B_(1)nnB_(2))=P(B_(1))P(B_(2)//B_(1))=3/5xx5/9=1/3`