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 [tex]\times[/tex] Probability that second person is hopelessly romantic
= [tex]P(R) \times P(R)[/tex]
= 0.13 [tex]\times[/tex] 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
= [tex]1 - (P(R') \times P(R'))[/tex]
= 1 - (0.87 [tex]\times[/tex] 0.87)
= 1 - 0.7569 = 0.2431
