Asked by Jeff
There are 4 white socks and 4 black socks. You randomly divides socks into pairs. What is the probability that each pair consists of 2 socks of the same colour? Express answer as a fraction.
I'm not really sure how to start this question.
I'm not really sure how to start this question.
Answers
Answered by
Steve
well, using brute force, just list the ways you could pair up the socks.
How many of those ways fit the requirements?
How many of those ways fit the requirements?
Answered by
Farohw
There are a total of 8 socks: 4 white and 4 black. Two are randomly selected. Therefore, 8C2 or C(8,2) = 28
Out of 4 white socks, 2 white socks can be selected in 4C2 ways or C(4,2) = 6.
Out of 4 black socks, 2 black socks can be selected in 4C2 or C(4,2) = 6.
Total number of ways of selecting the same color: 6 + 6 = 12.
Probability of getting both socks of same color = 12/28 = 3/7
Alternatively, you can say there are a total of 8 socks of which 4/8 are white and 4/8 are black. To find the same color:
White socks: (4/8)*(3/7) = 3/14
Black socks: (4/8)*(3/7) = 3/14
Then, add the two probabilities: 3/14 + 3/14 = 6/14
Reduce 6/14 = 3/7 which is the same answer as above.
Out of 4 white socks, 2 white socks can be selected in 4C2 ways or C(4,2) = 6.
Out of 4 black socks, 2 black socks can be selected in 4C2 or C(4,2) = 6.
Total number of ways of selecting the same color: 6 + 6 = 12.
Probability of getting both socks of same color = 12/28 = 3/7
Alternatively, you can say there are a total of 8 socks of which 4/8 are white and 4/8 are black. To find the same color:
White socks: (4/8)*(3/7) = 3/14
Black socks: (4/8)*(3/7) = 3/14
Then, add the two probabilities: 3/14 + 3/14 = 6/14
Reduce 6/14 = 3/7 which is the same answer as above.
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