Question

An insurance company believes that people can be divided into two classes: accident-prone and non-accident-prone. If 30% of the population is accident-prone and the probability of having an accident within a year is 0.4 for accident-prone and 0.2 for non-accident-prone, what is the probability that a new policyholder will have an accident within a year?

a. 0.1
b. 0.15
c. 0.2
d. 0.25

Answer 1

The probability that a new policyholder will have an accident within a year is 0.26.

Step-by-step explanation:

To find the probability that a new policyholder will have an accident within a year, we need to consider the probabilities for accident-prone and non-accident-prone individuals, as well as the percentage of the population that falls into each category.

Given that 30% of the population is accident-prone, and the probability of having an accident within a year is 0.4 for accident-prone and 0.2 for non-accident-prone individuals, we can calculate the overall probability using the law of total probability:

(0.4 * 0.3) + (0.2 * 0.7) = 0.12 + 0.14 = 0.26

Therefore, the probability that a new policyholder will have an accident within a year is 0.26.