Question

Jim's 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?
A) 2/13
B) 11/13
C) 4/13
D) 1/16

Answer 1

11/13
there are 13 socks left and 2 are green

Answer 2

Answer: Option 'B' is correct.

Step-by-step explanation:

Since we have given that

Number of pairs of black socks = 2

Number of pairs of white socks = 3

Number of pair of green = 1

Number of pair of gray = 2

Number of black socks = 2×2=4

Number of white socks = 3×2 = 6

Number of green socks = 1×2=2

Number of gray socks = 2×2=4

Total number of socks = 4+6+2+4=16

Since he picked 1 black, 1 white and 1 gray.

So, Remaining socks = 16-3=13

To make a complete pair it must be of black, or white or gray color.

So, Possible outcomes = 13-2=11 (deducting the outcomes of green color)

So, Probability that he will have a complete pair is given by

$\dfrac{11}{13}$

Hence, Option 'B' is correct.