Question

Kevin is trying to find a white sock in a drawer. He has 16 white socks, 4 brown socks, and 6 black socks. What is the probability that he pulls out a black or brown sock, puts it back and then pulls out a white sock?

Answer 1

`Probability=(40)/(169)`

Explanation:

`White(W)\ socks=16\\Brown(B)\ Socks=4\\Black(Bl) Socks=6\\Total(T) Socks=26\\`

First Event: Black or brown Sock

`n(B\cup Bl)=10`

`P(B\cup Bl)=(n(B\cup Bl))/(n(T))=(10)/(26)`

Second Event: White Sock

`n(W)=16\\n(T)=26\\\\P(W)=(n(W))/(n(T))=(16)/(26)`

These two events are independent Hence probability that first sock is black or brown and second is white
`=(10)/(26)* (16)/(26)=(40)/(169)\approx 0.2367`