Question

In a certain town, 45% of the population have dimples (and the rest do not) and 70% have a widow'speak (and the rest do not). Assuming that these physical traits are independent, what is theprobability that a randomly selected person has neither dimples nor a widow's peak?

Answer 1

16.5%

Step-by-step explanation:

First, we need to find the probability that a person doesn't have dimples, so it is equal to:

P(No dimples) = 100% - 45% = 55%

Because this probability is the complement of the probability to have dimples.

In the same way, the probability that a person doesn't have a widow's peak is equal to:

P( no widow's peak) = 100% - 70% = 30%

Then, if two events are independent, the probability that they happen at the same time is:

P(A ∩ B) = P(A) P(B)

Therefore, the probability that a randomly selected person has neither dimples nor a widow's peak is:

P = 0.55(0.3) = 0.165 = 16.5%

Then, the answer is 16.5%