Question

An actuary studied the likelihood that different types of drivers have at least one collision during any one-year period. The results of the study appear below. Type Percentage Collision % Teen 7 15 Young adult 18 6 Middle aged adult 41 5 Senior 34 8 Find the probability that a driver with at least one collision in the past year is a Teen driver.

Answer 1

The probability that a driver with at least one collision in the past year is a Teen driver is 7%.

Step-by-step explanation:

The probability that a driver with at least one collision in the past year is a Teen driver can be found by using conditional probability. We can use the formula:

P(Teen|Collision) = P(Teen ∩ Collision) / P(Collision)

Given that Teen drivers make up 7% of all drivers and the collision rate for all drivers is 15%, we have:

P(Teen|Collision) = (0.07 * 0.15) / 0.15 = 0.07

Therefore, the probability that a driver with at least one collision in the past year is a Teen driver is 0.07 or 7%.