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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