About 9% 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 that at least one is hopelessly romantic? A) The probability that both will be hopelessly romantic is . (Round 4 decimal places as needed).
B) The probability that at least one person is hopelessly romantic is .

A. 0.0081

B. 0.1638

Step-by-step explanation:

From the question, we are told that 9% of the population are hopelessly romantic.

The percentage that are not hopelessly romantic = 100-9 = 91%

The probability of choosing a hopelessly romantic person = 9% = 9/100 = 0.09

The probability of choosing a person who is not hopelessly romantic = 91% = 91/100 = 0.91

Now, we want to select two people and calculate the following probability;

1. Both will be hopelessly romantic

Let’s have the people as A and B

The probability that both will be hopelessly romantic will the the product of being hopelessly romantic probability = 0.09 * 0.09 = 0.0081

b. Probability that at least one person is hopelessly romantic

What this means is that the probability that one of the two ONLY is hopelessly romantic;

We can have two cases here;

Probability (That A is hopelessly while B is not )or Probability (A is not and B is hopeless )

Thus we have :

(0.09 * 0.91) + (0.91 * 0.09) = 0.0819 * 2 = 0.1638

it would be 6xy and -16xy.