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?

Answer 1

The probability that Jim will have a complete pair if he picks another sock randomly is 0.85.

Calculation of probability after picking randomly without replacement

After picking 1 black, 1 white, and 1 gray sock without putting them back, we have:

B = Number of black sock = (2 * 2) – 1 = 3

W = Number of white sock = (2 * 3) – 1 = 5

G = Number of green sock = 2 * 1 = 2

Gy = Number of grey sock = (2 * 2) – 1 = 3

T = Total number of sock = B + W + G + Gy = 3 + 5 + 2 + 3 = 13

The probability that Jim will have a complete pair if he picks another sock randomly can be calculated as follows:

C = Probability that Jim will have a complete pair = (B + W + Gy) / T

C = (3 + 5 + 3) / 13

C = 11 / 13, or 0.85

Learn more about probability here: https://brainly.com/question/16255131.

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