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what is the probability that in a group of 5 people chosen at random, there are at least two born on the same day of the week?

Sagot :

Therefore , the probability of at least two born on the same day of the week is  0.143

What is probability?

Probability is the possibility that an event will happen.This could mean that something is definitely going to happen, that it has a chance of happening, or that it is impossible. Mathematically, probability is quantified on a scale from 0 to 1.

Given:

group of 5 people at random.

We used the formula for the conditional probability

The conditional probability is,

P(A|B)=P(AUB)/P(A)

The complement rule of probability, which is the second, is

P(E) = 1 - P(e)

Calculate one by one

a) Since a week has seven days and the first person has seven possible birth dates, the likelihood of that person is:

P(1st person) = 7/7 = 1

The second person now gets the same possibilities as person 1, but he or she must match that person's day, therefore there is only one option out of seven that fits that criteria, as follows:

P(A|B) = 1/7

Then the probability is

P = 1 * 1/7 = 1/7 or 0.143

Therefore , the probability of at least two born on the same day of the week is  0.143

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