Question
A dresser drawer contains one pair of socks with each of the following colors: blue, brown, red, white and black.
Each pair is folded together in a matching set.
You reach into the sock drawer and choose a pair of socks without looking.
You replace this pair and then choose another pair of socks.
What is the probability that you will choose the red pair of socks both times?
A. 1/25
B. 1/5
C. 2/25
D. 1/4
Answers
GPT-4o mini
To find the probability of selecting the red pair of socks both times when drawing randomly, we can follow these steps:
1. **Calculate the probability of choosing the red pair of socks on the first draw.**
There are 5 pairs of socks (one of each color), so the probability of picking the red pair on the first draw is:
\[
P(\text{red on first draw}) = \frac{1}{5}
\]
2. **Since you replace the pair of socks after the first draw, the situation is the same for the second draw.** Therefore, the probability of picking the red pair on the second draw is also:
\[
P(\text{red on second draw}) = \frac{1}{5}
\]
3. **Since the draws are independent, the combined probability of both events (choosing red socks both times) is the product of their individual probabilities:**
\[
P(\text{red both times}) = P(\text{red on first draw}) \times P(\text{red on second draw}) = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25}
\]
Thus, the probability that you will choose the red pair of socks both times is \(\frac{1}{25}\).
Therefore, the correct answer is **A. 1/25**.
1. **Calculate the probability of choosing the red pair of socks on the first draw.**
There are 5 pairs of socks (one of each color), so the probability of picking the red pair on the first draw is:
\[
P(\text{red on first draw}) = \frac{1}{5}
\]
2. **Since you replace the pair of socks after the first draw, the situation is the same for the second draw.** Therefore, the probability of picking the red pair on the second draw is also:
\[
P(\text{red on second draw}) = \frac{1}{5}
\]
3. **Since the draws are independent, the combined probability of both events (choosing red socks both times) is the product of their individual probabilities:**
\[
P(\text{red both times}) = P(\text{red on first draw}) \times P(\text{red on second draw}) = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25}
\]
Thus, the probability that you will choose the red pair of socks both times is \(\frac{1}{25}\).
Therefore, the correct answer is **A. 1/25**.