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

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.

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

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

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

We want P(X > 0). So

In which

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