A drawer contains 2 black sock, 8 gray saocks, and 3 blue socks. Without lookign you draw out a sock and the4n draw out a second sock without returning the first sock. What is the probability that the two socks you draw arer a matching pair?
7/22
To calculate the probability of drawing a matching pair of socks, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes can be found by multiplying the number of choices for the first sock by the number of choices for the second sock. In this case, there are 13 socks to choose from initially, so there are 13 choices for the first sock. After drawing one sock, there are 12 socks left, so there are 12 choices for the second sock.
The number of favorable outcomes (matching pair) depends on the color of the first sock. We need to consider three scenarios:
1. If the first sock drawn is black, there is only one other black sock left in the drawer, resulting in 1 favorable outcome (matching pair).
2. If the first sock drawn is gray, there are 7 other gray socks left in the drawer, resulting in 7 favorable outcomes (matching pair).
3. If the first sock drawn is blue, there are 2 other blue socks left in the drawer, resulting in 2 favorable outcomes (matching pair).
So, the total number of favorable outcomes is 1 + 7 + 2 = 10.
Therefore, the probability of drawing a matching pair of socks is 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)
= 10 / (13 * 12)
≈ 0.641
Hence, the probability of drawing a matching pair of socks is approximately 0.641, or 64.1%.