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.