Question

13.
A basket contains 11 pieces of fruit: 4 apples, 5 oranges, and 2 bananas. Jonas takes a piece of fruit at random from the basket, and then Beth takes a piece at random. What is the probability that Jonas will get an orange and Beth will get an apple?

Answer 1

To find the probability that Jonas will get an orange and Beth will get an apple, we need to calculate the probability of each event happening in sequence.

**Step 1: Calculate the probability that Jonas gets an orange.**

The total number of pieces of fruit in the basket is 11 (4 apples + 5 oranges + 2 bananas).

The number of oranges is 5.

The probability that Jonas picks an orange is:

\[
P(\text{Jonas gets an orange}) = \frac{\text{Number of oranges}}{\text{Total number of fruits}} = \frac{5}{11}
\]

**Step 2: Calculate the probability that Beth gets an apple after Jonas has taken an orange.**

After Jonas picks an orange, there are now 10 pieces of fruit left in the basket (4 apples, 4 oranges, and 2 bananas).

Now, the number of apples is still 4.

The probability that Beth picks an apple after Jonas has picked an orange is:

\[
P(\text{Beth gets an apple} \mid \text{Jonas got an orange}) = \frac{\text{Number of apples}}{\text{Total remaining fruits}} = \frac{4}{10} = \frac{2}{5}
\]

**Step 3: Calculate the overall probability that Jonas gets an orange and Beth gets an apple.**

Since both events (Jonas picking an orange and Beth picking an apple) are independent events, we multiply their probabilities:

\[
P(\text{Jonas gets an orange and Beth gets an apple}) = P(\text{Jonas gets an orange}) \times P(\text{Beth gets an apple} \mid \text{Jonas got an orange})
\]

Substituting the probabilities we calculated:

\[
P(\text{Jonas gets an orange and Beth gets an apple}) = \frac{5}{11} \times \frac{2}{5}
\]

Calculating this gives:

\[
= \frac{5 \times 2}{11 \times 5} = \frac{10}{55} = \frac{2}{11}
\]

Thus, the final probability that Jonas will get an orange and Beth will get an apple is:

\[
\boxed{\frac{2}{11}}
\]