Your sock drawer if full of unmatched socks. There are 4 white sock, 4 brown socks, and 4 green socks. You randomly pick one sock out then another. What is the probability that you get a matching pair of green socks?
12 socks in all, so
4/12 * 3/11
(assuming all the green socks match each other ...)
To calculate the probability of getting a matching pair of green socks, we need to find the total number of possible outcomes and the number of favorable outcomes.
Total number of possible outcomes:
When you randomly pick one sock out and then another, there are 12 socks in total in the drawer. After the first sock is picked, there will be 11 socks left, so the total number of pairs that can be formed is 12 * 11 = 132.
Number of favorable outcomes:
To have a matching pair of green socks, you need to pick two green socks. There are 4 green socks in the drawer, so the number of favorable outcomes is the number of ways to choose 2 green socks from a total of 4, which is denoted as C(4, 2) or 4 choose 2.
Using the formula for combinations, C(n, r) = n! / ((n-r)! * r!):
C(4, 2) = 4! / ((4-2)! * 2!)
= 4! / (2! * 2!)
= 24 / (2 * 2)
= 6
Therefore, the number of favorable outcomes is 6.
Probability of getting a matching pair of green socks:
The probability can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 6 / 132
= 1 / 22
So, the probability of getting a matching pair of green socks when randomly picking two socks is 1/22 or approximately 0.045.
To solve this probability problem, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of possible outcomes. When you pick the first sock, there are 12 socks in the drawer. Since you randomly select one sock, there are 12 options. When you pick the second sock, there will be 11 socks remaining in the drawer, so there are 11 options.
The total number of possible outcomes is calculated by multiplying the number of options for the first pick (12) by the number of options for the second pick (11), which is equal to 12 * 11 = 132.
Now, let's calculate the number of favorable outcomes. To get a matching pair of green socks, you need to pick two green socks from the drawer. There are 4 green socks in total. For the first pick, you have 4 options, and for the second pick, you have 3 options (since you have already removed one green sock from the drawer).
The number of favorable outcomes is calculated by multiplying the number of options for the first green sock pick (4) by the number of options for the second green sock pick (3), which is equal to 4 * 3 = 12.
Finally, we can calculate the probability of getting a matching pair of green socks by dividing the number of favorable outcomes (12) by the total number of possible outcomes (132):
Probability = favorable outcomes / total outcomes = 12 / 132 = 1 / 11
Therefore, the probability of getting a matching pair of green socks is 1/11 or approximately 0.0909 (rounded to four decimal places).