Question

About 16% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? W
is the probability at least one is hopelessly romantic? Assume the events are independent
(a) The probability that both will be hopelessly romantic is___
(Round to four decimal places as needed.)
(b) The probability that at least one person is hopelessly romantic is__
(Round to four decimal places as needed.)

Answer 1

Answer:

Here, 16 % of the total population of a large country is hopelessly romantic.

.

Assuming events are independent,

Probability of a person who is hopelessly romantic = 16% = 16/100

(a) Probability of both will be hopelessly

romantic =

$\frac{16}{100} \times \frac{16}{100}$

$\frac{256}{10000}$

= 0.0256...ans

Probability that are not hopelessly

romantic = 100% - 16%= 84%

$\frac{84}{100} \times \frac{84}{100}$

$\frac{7056}{10000}$

= 0.7056

(b) So, the probability of atleast one is hopelessly romantic = 1 - 0.7056

= 0.2944...ans

.

Hope it helps!