The weather report for this work week (Monday through Friday) states that the probability of rain is 5% for each day. The probability that i

Question

The weather report for this work week (Monday through Friday) states that the probability of rain is 5% for each day. The probability that it will rain at least once this working week is: ____________

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Brielle 2 days 2021-09-11T22:13:33+00:00 1 Answer 0

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    2021-09-11T22:14:53+00:00

    Answer:

    22.62%

    Step-by-step explanation:

    For each day, there are only two possible outcomes. Either it rains, or it does not. The probability of rain on a given day is independent from other days. So we use the binomial probability distribution to solve this question.

    Binomial probability distribution

    The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

    C_{n,x} = \frac{n!}{x!(n-x)!}

    And p is the probability of X happening.

    The weather report for this work week (Monday through Friday) states that the probability of rain is 5% for each day.

    5 days, 5% each day.

    So p = 0.05, n = 5

    The probability that it will rain at least once this working week is:

    Either it does not rain on any day, or it rains in at least one day. The sum of the probabilities of these events is decimal 1. So

    P(X = 0) + P(X > 0) = 1

    We want P(X > 0). So

    P(X > 0) = 1 - P(X = 0)

    In which

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    P(X = 0) = C_{5,0}.(0.05)^{0}.(0.95)^{5} = 0.7738

    P(X > 0) = 1 - P(X = 0) = 1 - 0.7738 = 0.2262

    22.62% probability that it will rain at least once this working week is:

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45:7+7-4:2-5:5*4+35:2 =? ( )