A drawer contains 9 black socks, 8 gray socks, and 7 blue socks. Without looking, you draw out a sock and then draw out a second sock without returning the first sock. What is the probability that the two socks you draw are the same color?

Question

Aidyn Morrow

Mathematics

17 January, 19:13

A drawer contains 9 black socks, 8 gray socks, and 7 blue socks. Without looking, you draw out a sock and then draw out a second sock without returning the first sock. What is the probability that the two socks you draw are the same color?

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Answers (1)

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Maximilian Bennett · Answer 1

HI!

First of all, there are total 9 + 8 + 7 = 24 socks.

Probability of a black socks in a row is 9/24

Probability of the second black socks without replacement, if first one was black, is 8/23

Therefore the probability of the 2 black socks in a row are 3/23 (I multiplied the two)

Using the same technique, the p of 2 gray socks are 7/69

The p of 2 blue socks are 7/92

Now you add them up, and you get 85/276 as your answer

Let me know if there are any other questions!