Question 28
In a drawer, there are 13 pairs of socks, 6 of which are white, and 8 t-shirts, 4 of which are
white. If you randomly select one pair of socks and one t-shirt, what is the probability that
both are white? Express your answer as a reduced fraction.

Question

UpStudy AI · Accepted Answer

To find the probability that both the selected pair of socks and the selected t-shirt are white, we can use the following steps:

1. **Determine the total number of pairs of socks and t-shirts:**
   - Total pairs of socks = 13
   - Total t-shirts = 8

2. **Determine the number of white pairs of socks and t-shirts:**
   - White pairs of socks = 6
   - White t-shirts = 4

3. **Calculate the probability of selecting a white pair of socks:**
   $$
   P(\text{white socks}) = \frac{\text{Number of white socks}}{\text{Total pairs of socks}} = \frac{6}{13}
   $$

4. **Calculate the probability of selecting a white t-shirt:**
   $$
   P(\text{white t-shirt}) = \frac{\text{Number of white t-shirts}}{\text{Total t-shirts}} = \frac{4}{8} = \frac{1}{2}
   $$

5. **Calculate the probability that both the selected pair of socks and the selected t-shirt are white:**
   Since the selection of socks and t-shirts are independent events, we can multiply their probabilities:
   $$
   P(\text{both white}) = P(\text{white socks}) \times P(\text{white t-shirt}) = \frac{6}{13} \times \frac{1}{2}
   $$

6. **Perform the multiplication:**
   $$
   P(\text{both white}) = \frac{6 \times 1}{13 \times 2} = \frac{6}{26}
   $$

7. **Reduce the fraction:**
   $$
   \frac{6}{26} = \frac{3}{13}
   $$

Thus, the probability that both the selected pair of socks and the selected t-shirt are white is $$\frac{3}{13}$$.
The probability that both the selected pair of socks and the selected t-shirt are white is $$\frac{3}{13}$$.

Question 28
In a drawer, there are 13 pairs of socks, 6 of which are white, and 8 t-shirts, 4 of which are
white. If you randomly select one pair of socks and one t-shirt, what is the probability that
both are white? Express your answer as a reduced fraction.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Probability Questions

Question 28 In a drawer, there are 13 pairs of socks, 6 of which are white, and 8 t-shirts, 4 of which are white. If you randomly select one pair of socks and one t-shirt, what is the probability that both are white? Express your answer as a reduced fraction.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Probability Questions

Question 28
In a drawer, there are 13 pairs of socks, 6 of which are white, and 8 t-shirts, 4 of which are
white. If you randomly select one pair of socks and one t-shirt, what is the probability that
both are white? Express your answer as a reduced fraction.