select the correct answer. jims sock drawer has two pairs of black socks, three pairs of white, one pair of…

select the correct answer. jims sock drawer has two pairs of black socks, three pairs of white, one pair of green, and two pairs of gray. one evening he randomly picks three socks assuming that he will get a matched pair, but instead turns up with 1 black, 1 white, and 1 gray sock. without putting back the socks he picked, he picks another sock randomly. what is the probability that he will have a complete pair?\na. $\frac{2}{13}$\nb. $\frac{11}{13}$\nc. $\frac{4}{13}$\nd. $\frac{1}{16}$

select the correct answer. jims sock drawer has two pairs of black socks, three pairs of white, one pair of green, and two pairs of gray. one evening he randomly picks three socks assuming that he will get a matched pair, but instead turns up with 1 black, 1 white, and 1 gray sock. without putting back the socks he picked, he picks another sock randomly. what is the probability that he will have a complete pair?\na. $\frac{2}{13}$\nb. $\frac{11}{13}$\nc. $\frac{4}{13}$\nd. $\frac{1}{16}$

Answer

Explanation:

Step1: Calculate total number of socks initially

Jim has (2\times2 + 3\times2+1\times2 + 2\times2=4 + 6+2 + 4 = 16) socks initially. After picking 3 socks, there are (16 - 3=13) socks left.

Step2: Analyze favorable cases for a pair

He has 1 black, 1 white and 1 gray sock already. To get a pair, he needs to pick a black, white or gray sock. There are ((2\times2 - 1)+(3\times2 - 1)+(2\times2 - 1)=3 + 5+3 = 11) such socks among the remaining 13 socks.

Answer:

B. (\frac{11}{13})