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A bowl of fruits contains bananas, oranges, apples, and pears.
A photo shows a bowl containing bananas, apples, pears, and oranges.
Source: Robyn Mackenzie/Shutterstock
You choose a fruit from the bowl without looking. Do you think each fruit will be equally likely to be selected? Why or why not? How likely will you select a banana? Is it likely that you will select an orange? What do you need to know in order to determine the likelihood of selecting a pear? If there are 24 pieces of fruit in the bowl, what is the likelihood of selecting a pear or an apple? If you select two fruit without replacement, what is the chance that you will have an orange and a banana? What affects the outcome of these choices?
Each fruit in the bowl should be equally likely to be selected, assuming that they are all mixed together well and there is no bias in how they are arranged. So the likelihood of selecting a banana should be 1/4, as there are four types of fruit in the bowl.
To determine the likelihood of selecting a pear, you would need to know how many pears are in the bowl compared to the total number of fruit. If there are 6 pears (for example) out of the 24 total pieces of fruit, then the likelihood of selecting a pear would be 6/24 or 1/4.
If you want to calculate the likelihood of selecting a pear or an apple, you would add the individual probabilities together since they are not mutually exclusive events. So if there are 8 apples and 6 pears out of the 24 total fruit, then the likelihood of selecting a pear or an apple would be (8 + 6)/24 or 14/24.
If you select two fruit without replacement, the likelihood of having an orange and a banana would depend on how many oranges and bananas are in the bowl, as well as the total number of fruit left after the first selection. The outcomes of these choices would be affected by the initial composition of the bowl and the choices made during the selection process.