Question

you own 17 pairs of socks, with each pair being a different color. a robber breaks into your house and randomly grabs 6 socks from your sock drawer, regardless of whether they are matching or not. (a) suppose one of the 17 pairs is blue. what is the probability that you still own a complete pair of blue socks after the robbery?

Answer 1

To calculate the probability of still having a complete pair of blue socks after the robbery, we can use the complement rule and calculate the probability of not getting any blue socks. By subtracting this probability from 1, we find that the probability of still owning a complete pair of blue socks is 20.1%.

Step-by-step explanation:

To solve this problem, we need to calculate the probability of still having a complete pair of blue socks after the robbery. Let's break it down:

1. There are a total of 17 pairs of socks, which means a total of 34 socks.
2. The robber randomly grabs 6 socks from the drawer.
3. Since one of the pairs is blue, we need to find the probability that at least one of the 6 socks is blue.
4. We can use the complement rule to find this probability: 1 - P(no blue socks)
5. P(no blue socks) = (32/34) * (31/33) * (30/32) * (29/31) * (28/30) * (27/29)
6. Therefore, P(at least one blue sock) = 1 - P(no blue socks)

Calculating the probabilities, we find that the probability of still owning a complete pair of blue socks after the robbery is approximately 0.201 or 20.1%.