Question

Your teacher is giving out fruit for lunch. A paper bag contains 4 apples, 6 pears, and 8 oranges.

What is the probability you will pick an orange at random?


What is the complement to this event?
✔ Pulling either an apple or a pear from the bag


What is the probability of the complement?


Which fruit is more likely to be chosen?

Answer 1

To determine the probability of picking an orange from the bag, let's first calculate the total number of fruits in the bag:

- Number of apples = 4
- Number of pears = 6
- Number of oranges = 8

Total number of fruits = 4 (apples) + 6 (pears) + 8 (oranges) = 18 fruits

### Probability of Picking an Orange

The probability of picking an orange at random is calculated as follows:

\[
\text{Probability of picking an orange} = \frac{\text{Number of oranges}}{\text{Total number of fruits}} = \frac{8}{18} = \frac{4}{9}
\]

### Probability of the Complement

The complement of picking an orange is picking either an apple or a pear. To find the probability of this complement event, we can determine the number of apples and pears:

- Total number of apples and pears = 4 (apples) + 6 (pears) = 10

The probability of picking either an apple or a pear is:

\[
\text{Probability of picking an apple or a pear} = \frac{\text{Number of apples and pears}}{\text{Total number of fruits}} = \frac{10}{18} = \frac{5}{9}
\]

### Which Fruit is More Likely to be Chosen?

To determine which fruit is more likely to be chosen, we compare the probabilities:

- Probability of picking an orange = \(\frac{4}{9}\)
- Probability of picking an apple or a pear = \(\frac{5}{9}\)

Since \(\frac{5}{9}\) (the probability of picking an apple or pear) is greater than \(\frac{4}{9}\) (the probability of picking an orange), it is more likely that you will pick either an apple or a pear from the bag.