## About 19% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both a

Question

About 19% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic?

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Math
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2021-09-15T22:05:39+00:00
2021-09-15T22:05:39+00:00 1 Answer
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## Answers ( )

Answer:3.61% probability that both are hopelessly romantic.

34.39% probability at least one is hopelessly romantic

Step-by-step explanation:For each person, there are only two possible outcomes. Either they are hopelessly romantic, or they are not. The probability of a person being hopelessly romantic is independent from other people. So we use the binomial probability distribution to solve this question.

Binomial probability distributionThe 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.

19% of the population of a large country is hopelessly romantic.This means that

Two people are randomly selectedThis means that

What is the probability both are hopelessly romantic?This is P(X = 2). So

3.61% probability that both are hopelessly romantic.

What is the probability at least one is hopelessly romantic?34.39% probability at least one is hopelessly romantic