Question

Martin puts two bowls of fruit out for his friends. The bowl of grapes has 9 green grapes and 16 red grapes. The bowl of tangerines has 7 seeded and 3 seedless tangerines.
Martin's friend chooses a random grape and a random tangerine. What is the probability that she chooses a green grape and a seedless tangerine?

Answer 1

To calculate the probability of choosing a green grape and a seedless tangerine, we need to find the probabilities of each event separately and then multiply them together.

1. **Calculate the total number of grapes:**
- Green grapes: 9
- Red grapes: 16
- Total grapes = 9 + 16 = 25

2. **Calculate the probability of choosing a green grape:**
\[
P(\text{green grape}) = \frac{\text{number of green grapes}}{\text{total number of grapes}} = \frac{9}{25}
\]

3. **Calculate the total number of tangerines:**
- Seeded tangerines: 7
- Seedless tangerines: 3
- Total tangerines = 7 + 3 = 10

4. **Calculate the probability of choosing a seedless tangerine:**
\[
P(\text{seedless tangerine}) = \frac{\text{number of seedless tangerines}}{\text{total number of tangerines}} = \frac{3}{10}
\]

5. **Calculate the combined probability of choosing a green grape and a seedless tangerine:**
\[
P(\text{green grape and seedless tangerine}) = P(\text{green grape}) \times P(\text{seedless tangerine}) = \frac{9}{25} \times \frac{3}{10}
\]
\[
= \frac{9 \times 3}{25 \times 10} = \frac{27}{250}
\]

Thus, the probability that Martin's friend chooses a green grape and a seedless tangerine is

\[
\boxed{\frac{27}{250}}.
\]