There are 11 clean individual socks in your sock drawer. There is only one matching pair among them. In the dark, you reach into the drawer and randomly pick 2 socks. What is the probability that you choose the matching pair? Write your answer as a fraction in simplest form.
To find the probability of choosing the matching pair, we need to find the total number of possible outcomes and the number of desired outcomes.
Total number of possible outcomes:
When you randomly pick 2 socks from the drawer, the total number of possible outcomes is determined by the number of ways you can pick any 2 socks from the 11 available.
We can calculate this using the combinations formula, which is given by nCr = n! / (r!(n-r)!) where n is the total number of items and r is the number of items chosen.
In this case, we have 11 socks and we are choosing 2, so the total number of possible outcomes is:
11C2 = 11! / (2!(11-2)!) = 11! / (2!9!) = (11 * 10) / (2 * 1) = 55.
Desired outcome:
We want to choose the matching pair, which means picking 2 socks that belong to the same pair. Since there is only one matching pair among the 11 socks, we can represent this as 1 desired outcome.
Now, we can calculate the probability by dividing the number of desired outcomes by the total number of possible outcomes:
Probability = Desired outcomes / Total outcomes = 1/55.
Therefore, the probability of choosing the matching pair is 1/55.
there are 11C2 ways of picking to socks ... 11C2 = (11 * 10) / (2 * 1)
there is one way of selecting a matching pair
matching pairs / total pairs = ?