Respuesta :
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.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
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 [tex]p = 0.05, n = 5[/tex]
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
[tex]P(X = 0) + P(X > 0) = 1[/tex]
We want P(X > 0). So
[tex]P(X > 0) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.05)^{0}.(0.95)^{5} = 0.7738[/tex]
[tex]P(X > 0) = 1 - P(X = 0) = 1 - 0.7738 = 0.2262[/tex]
22.62% probability that it will rain at least once this working week is:
