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27 June, 13:48

On a particular day in July, there is a 20% probability of rain in Vancouver, a 65% probability of rain in Calgary, and a 75% probability of rain in Saskatoon. What is the probability that it will rain in all 3 cities on that day?

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  1. 27 June, 14:14
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    The probability that it will rain in all 3 cities on that day

    P (V∪ C∪S) = 0.93 = 93%

    Step-by-step explanation:

    Let 'V' be the event of rain in Vancouver

    Given that the probability of rain in Vancouver

    P (V) = 20% = 0.20

    P (V⁻) = 1 - P (V) = 1 - 0.20 = 0.80

    Let 'C' be the event of rain in Calgary

    Given that the probability of rain in Calgary

    P (C) = 65% = 0.65

    P (C⁻) = 1 - P (C) = 1 - 0.65 = 0.35

    Let 'S' be the event of rain in Saskatoon

    Given that the probability of rain in Saskatoon

    P (S) = 75% = 0.75

    P (S⁻) = 1 - P (S) = 1 - 0.75 = 0.25

    First we will prove that the probability that it will not rain in all 3 cities on that day

    P (V⁻ ∩ C⁻ ∩ S⁻) = P (V⁻) P (C⁻) P (S⁻)

    = 0.80 * 0.35 * 0.25

    = 0.07

    The probability that it will rain in all 3 cities on that day

    P (V∪ C∪S) = 1 - (P (V⁻ ∩ C⁻ ∩ S⁻)

    = 1 - 0.07

    = 0.93
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