There are 6 pairs of black socks and 6 pairs of white socksWhat is the probability to pick a pair of black or white socks when 2 socks are selected randomly in darkness?M
I think it's nCk which the total of socks would be 12 since we have 6 whites and 6 black. you would have to choose 2. in that case order does not matter and we use the combination formula 12C2 = 66 possible ways.
could be either BB or WW
Prob(BB) = (6/12)(5/11) = 5/22
which is the same as the prob(WW)
so prob of either WW or BB = 2(5/22) = 10/22
(note only other cases are WB and BW
and the prob of those = 2(6/12)(6/11) = 2/11 or 12/22
and prob of all cases = 10/22 + 12/22 = 22/22 = 1 )
All is good!
correction in 3rd last line, should be
and the prob of those = 2(6/12)(6/11) = 6/11 or 12/22
To find the probability of picking a pair of black or white socks when selecting 2 socks randomly in darkness, we first need to calculate the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
When selecting 2 socks randomly, there are a total of 12 socks to choose from initially.
Number of favorable outcomes:
To get a pair of black or white socks, we can either select two black socks, two white socks, or one black sock and one white sock.
- Selecting two black socks: There are 6 pairs of black socks, so the number of ways to choose 2 black socks is given by the combination formula: C(6, 2) = 6! / (2!(6 - 2)!) = 15.
- Selecting two white socks: Similarly, the number of ways to choose 2 white socks is also C(6, 2) = 15.
- Selecting one black sock and one white sock: We have 6 choices for selecting a black sock and 6 choices for selecting a white sock (since there are 6 pairs of each). This gives us a total of 6 * 6 = 36 possible outcomes when selecting one black and one white sock.
So, the total number of favorable outcomes is 15 + 15 + 36 = 66.
Now, let's calculate the probability.
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 66 / 66 = 1
Therefore, the probability of picking a pair of black or white socks when selecting 2 socks randomly in darkness is 1 or 100%.