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

Answer:

$Probability=\frac{40}{169}$

Step-by-step explanation:

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

First Event: Black or brown Sock

$n(B\cup Bl)=10$

$P(B\cup Bl)=\frac{n(B\cup Bl)}{n(T)}=\frac{10}{26}$

Second Event: White Sock

$n(W)=16\\n(T)=26\\\\P(W)=\frac{n(W)}{n(T)}=\frac{16}{26}$

These two events are independent Hence probability that first sock is black or brown and second is white$=\frac{10}{26}\times \frac{16}{26}=\frac{40}{169}\approx 0.2367$