Question

About 1313​% of the population of a large country is hopelessly romantichopelessly romantic. If two people are randomly​ selected, what is the probability both are hopelessly romantichopelessly romantic​? What is the probability at least one is hopelessly romantichopelessly romantic​?

Answer 1

Answer:

Probability both are hopelessly romantic = 0.0169

Probability at least one is hopelessly romantic = 0.2431

Step-by-step explanation:

We are given that about 1313​% of the population of a large country is hopelessly romantic.

Also, given two people are randomly​ selected.

Firstly, Let Probability that the population of a large country is hopelessly romantic = P(R) = 0.13

(a) Probability both are hopelessly romantic is given by = Probability that first person is hopelessly romantic $\times$ Probability that second person is hopelessly romantic

                         = $P(R) \times P(R)$

                         = 0.13 $\times$ 0.13 = 0.0169

(b) Now, Probability that the population of a large country is not hopelessly romantic = P(R') = 1 - P(R) = 1 - 0.13 = 0.87.

So, Probability at least one is hopelessly romantic is given by = 1 - Probability that none of them is hopelessly romantic

                         = $1 - (P(R') \times P(R'))$

                         = 1 - (0.87 $\times$ 0.87)

                         = 1 - 0.7569 = 0.2431