Question

Christine has 1 blue sock, 3 purple socks and 1 green sock in a box.

Christine takes one sock at random from the box, puts it back, and takes another sock from the box. Find the probability that Christine takes at least one blue sock.

Answer 1

To find the probability that Christine takes at least one blue sock, we can calculate the probability of the complement event, which is the probability of not getting any blue socks.

The total number of socks in the box is 1 (blue) + 3 (purple) + 1 (green) = 5 socks.

The probability of not getting a blue sock on the first draw is (4 socks that are not blue) / (5 total socks) = 4/5.

Since Christine puts the first sock back before the second draw, the probabilities are independent. Thus, the probability of not getting a blue sock on the second draw is also 4/5.

To find the probability of not getting a blue sock in both draws, we multiply the probabilities: (4/5) * (4/5) = 16/25.

Finally, to find the probability of getting at least one blue sock, we subtract the probability of not getting any blue sock from 1: 1 - 16/25 = 9/25.

Therefore, the probability that Christine takes at least one blue sock is 9/25.