Question

According to a paper in forensic science international genetics from 2019, in Iceland it is found that approximately 9.22% of the population has brown or hazel eyes. if ten people are randomly selected, what is the probability that at least one has brown or hazel eyes?

Answer 1

To find the probability that at least one person out of ten has brown or hazel eyes, we can use the concept of complementary probability. The probability that at least one person has brown or hazel eyes is 0.5902, or 59.02%.

Step-by-step explanation:

To find the probability that at least one person out of ten has brown or hazel eyes, we can use the concept of complementary probability. The complementary probability is the probability that the event does not occur. In this case, the event is having no person with brown or hazel eyes.

The probability that a person does not have brown or hazel eyes is 1 - 9.22% = 90.78%. Since the selection of individuals is independent, the probability that all ten individuals do not have brown or hazel eyes is (90.78%)^10 = 0.4098.

Therefore, the probability that at least one person has brown or hazel eyes is 1 - 0.4098 = 0.5902, or 59.02%.