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?
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?
Answers
GPT-4o mini
To find the probability of choosing the red pair of socks both times, we can approach this problem using the concept of probability.
1. **Total pairs of socks**: There are 5 pairs of socks in total: blue, brown, red, white, and black.
2. **Probability of choosing the red pair of socks the first time**:
- Since there are 5 pairs, the probability of choosing the red pair of socks on the first draw is:
\[
P(\text{First draw - Red}) = \frac{1}{5}
\]
3. **Probability of choosing the red pair of socks the second time**:
- After replacing the first pair, the situation resets and you're again faced with the same 5 pairs of socks. Therefore, the probability of choosing the red pair of socks on the second draw is also:
\[
P(\text{Second draw - Red}) = \frac{1}{5}
\]
4. **Combined probability**:
Since the events are independent (the outcome of the first draw does not affect the outcome of the second draw), we can multiply the probabilities of both events:
\[
P(\text{Both draws - Red}) = P(\text{First draw - Red}) \times P(\text{Second draw - Red}) = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25}
\]
Thus, the probability that you will choose the red pair of socks both times is \(\frac{1}{25}\).
1. **Total pairs of socks**: There are 5 pairs of socks in total: blue, brown, red, white, and black.
2. **Probability of choosing the red pair of socks the first time**:
- Since there are 5 pairs, the probability of choosing the red pair of socks on the first draw is:
\[
P(\text{First draw - Red}) = \frac{1}{5}
\]
3. **Probability of choosing the red pair of socks the second time**:
- After replacing the first pair, the situation resets and you're again faced with the same 5 pairs of socks. Therefore, the probability of choosing the red pair of socks on the second draw is also:
\[
P(\text{Second draw - Red}) = \frac{1}{5}
\]
4. **Combined probability**:
Since the events are independent (the outcome of the first draw does not affect the outcome of the second draw), we can multiply the probabilities of both events:
\[
P(\text{Both draws - Red}) = P(\text{First draw - Red}) \times P(\text{Second draw - Red}) = \frac{1}{5} \times \frac{1}{5} = \frac{1}{25}
\]
Thus, the probability that you will choose the red pair of socks both times is \(\frac{1}{25}\).