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22 February, 05:24

About 9 % of the population of a large country is allergic to pollen. If two people are randomly selected, what is the probability both are allergic to pollen ? What is the probability at least one is allergic to pollen ?

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  1. 22 February, 08:32
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    Probability of both people being allergic: 0.81%.

    Probability of at least one being allergic: 17.19%

    Step-by-step explanation:

    If the probability of one person being allergic to pollen is 9%, the probability of two people selected being both allergic is:

    0.09 * 0.09 = 0.0081 = 0.81%

    The probability of at least one being allergic can be calculated with 1 minus the probability of both not being allergic.

    If the probability of being allergic is 9%, the probability of not being allergic is (1 - 0.09) = 0.91 = 91%.

    So, the probability of both not being allergic is:

    0.91 * 0.91 = 0.8281

    Then, The probability of at least one being allergic is:

    1 - 0.8281 = 0.1719 = 17.19%
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