Question

4. Corey's sock drawer has 9 black socks, 10 white, 4 green, and 2 with pink flamingos. He randomly picks three socks assuming that he will get a matched pair, but instead turns up with 1 black, 1 white, and 1green sock. Without putting back the socks he picked, he picks another sock randomly. What is the probability that he will have a complete pair?SHOW WORK!

Answer 1

SOLUTION:

After picking 1 black, 1 white, and 1 green sock without a replacement, what was left is 8 black, 9 white, 3 green and 2 pink, a total of 22.

If he picks another sock randomly, the probability that he will have a complete pair is calculated thus;

Pr (Black) + Pr (White) + Pr (Green)

$\frac{8}{22}\text{ + }\frac{9}{22}\text{ + }\frac{3}{22}\text{ = }\frac{20}{22}\text{ = }\frac{10}{11}$

The probability that he will have a complete pair is 10/11