Question

Randy has 4 black socks, 3 brown socks, and 3 blue socks in his drawer. If he selects 2 socks at random, what is the probability that he will select a pair the same color?

Answer 1

The probability of selecting a black sock first is 4/10. Having selected a black sock the probability of selecting another black sock is 3/9. Therefore the probability of selecting a pair of black socks is
\[P(black\ pair)=\frac{4}{10}\times\frac{3}{9}\]
Do you follow so far?

Answer 2

Why isn't it 3/10?

Answer 3

Because after a black sock has been selected first there are 3 black socks remaining and 9 socks of all colors remaining.

Answer 4

Okay. Gotcha.

Answer 5

Good! the probability of selecting a brown sock first is 3/10 and the probability of selecting another brown sock next is 2/9. So the probability of selecting a pair of brown socks is
\[P(brown\ pair)=\frac{3}{10}\times\frac{2}{9}\]
Can you now see what the probability of selecting a blue pair will be?

Answer 6

\[\frac{ 2 }{ 10 } \times\frac{ 1}{ 9 }\]

Answer 7

Not really. The probability of selecting a blue pair is the same as the probability of selecting a brown pair, the reason being that at the start there is the same number of blue socks (3) as brown socks (also 3). When looking at the probabilities of a black or brown or blue pair we start with all 10 socks to begin with.

Answer 8

Right.

Answer 9

The events 'select a black pair', 'select a brown pair' and 'select a blue pair' are mutually exclusive, meaning they can't happen at the same time. Therefore the probability of selecting a black pair or a brown pair or a blue pair is the sum of the individual probabilities:
\[P(pair\ black\ brown\ blue)=\frac{4\times3}{10\times9}+\frac{3\times2}{10\times9}+\frac{3\times2}{10\times9}=you\ can\ calculate\]

Answer 10

4/15?

Answer 11

Good work! You are correct :)

Answer 12

Thank you so much!

Answer 13

You're welcome :)