Asked by Dill
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 have no idea where to even start.
I have no idea where to even start.
Answers
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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.