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24 July, 21:14

For a certain weekend, the weatherman predicts that it will rain with a 40% probability on Saturday and a 50% probability on Sunday. Assuming these probabilities are independent, what is the probability that it rains over the weekend (that is, on at least one of the days) ? Express your answer as a percentage.

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  1. 25 July, 00:05
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    70%

    Step-by-step explanation:

    The probability it rains on at least one of the days is:

    P = P (Sat & not Sun) + P (Sun & not Sat) + P (Sat & Sun)

    P = (0.40) (1-0.50) + (0.50) (1-0.40) + (0.40) (0.50)

    P = 0.20 + 0.30 + 0.20

    P = 0.70

    Another way to look at it is 1 - the probability that it doesn't rain on either day.

    P = 1 - P (not Sat & not Sun)

    P = 1 - (1-0.40) (1-0.50)

    P = 1 - 0.30

    P = 0.70

    There is a 70% probability that it will rain on at least one day.
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