Question

A basket of fruits contains 5 apples n 3 pears. Sharon took 2 fruits @ all random. Wut is da probability dat both fruits r apples? Write ur answer in da simplest form of fraction

Answer 1

To find the probability that both fruits drawn are apples, we can use combinatorial counting.

1. **Total fruits in the basket**:
- 5 apples + 3 pears = 8 fruits.

2. **Total ways to choose 2 fruits from 8**:
\[
\text{Total ways to choose 2 fruits} = \binom{8}{2} = \frac{8 \times 7}{2 \times 1} = 28.
\]

3. **Total ways to choose 2 apples from 5**:
\[
\text{Total ways to choose 2 apples} = \binom{5}{2} = \frac{5 \times 4}{2 \times 1} = 10.
\]

4. **Probability of choosing 2 apples**:
\[
\text{Probability} = \frac{\text{Ways to choose 2 apples}}{\text{Total ways to choose 2 fruits}} = \frac{10}{28}.
\]

5. **Simplifying the fraction**:
\[
\frac{10}{28} = \frac{5}{14}.
\]

Thus, the probability that both fruits taken are apples is \(\frac{5}{14}\).