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.
first one you must pick the one of the two in the 11
2/11
the second pick you must pick the right one of the teen remaining
1/10
they are independent picks
so
2/11 * 1/ 10 = 0.181818182 or 1/55
Ah, the classic sock conundrum! Let's do the math with a splash of humor, shall we?
Well, the first sock you pick can be any of the 11 socks. But out of the remaining socks, only one will match the first sock you picked. So the probability of picking the matching pair on the first try is 1/11.
Now, onto the second sock! After picking the first sock, there will be 10 socks left in the drawer, including the one that matches the first sock. So, the probability of picking the matching pair on the second try is 1/10.
To find the overall probability, we multiply the probabilities of picking the matching pair on the first and second try together: (1/11) * (1/10) = 1/110.
Therefore, the probability of randomly choosing the matching pair of socks from your sock drawer is a humbly humorous 1/110.
To find the probability of choosing the matching pair, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Since there is only one matching pair among the 11 socks, the number of favorable outcomes is 1.
To calculate the total number of possible outcomes, we need to consider that we are choosing 2 socks from a pool of 11. This can be done using the combination formula.
The total number of possible outcomes is given by:
C(11, 2) = 11! / (2!(11-2)!) = 55
Therefore, the probability of choosing the matching pair is:
Probability = (Number of favorable outcomes) / (Total number of possible outcomes)
Probability = 1 / 55
Hence, the probability of choosing the matching pair is 1/55.
To find the probability of choosing the matching pair, we need to first determine the total number of ways to choose 2 socks out of the 11 available. Then, we need to determine the number of ways to choose the matching pair.
The total number of ways to choose 2 socks out of 11 can be calculated using the combination formula, denoted as C(n, r), where n is the total number of socks and r is the number of socks we are selecting.
In this case, we have 11 socks and we want to choose 2, so the formula becomes:
C(11, 2) = 11! / (2!(11-2)!) = 55
Now let's determine the number of ways to choose the matching pair. Since there is only 1 matching pair, we need to choose both of those socks among the 11 available. This can be done in only one way.
Therefore, the probability of choosing the matching pair is:
1 / 55
So, the answer is 1/55.
first one you must pick the one of the two in the 11
2/11
the second pick you must pick the right one of the teen remaining
1/10
they are independent picks
so
2/11 * 1/ 10 = 2/100 = 1/????