Question

an insurance company has the following information about drivers aged 16 to 18 years: 20% are involved in accidents each year; 10% are honor students; among those involved in an accident, 5% are honor students. let h be the event that a young driver is an honor student and a be the event that a young driver is involved in an accident. (a) state the probabilities given in terms of events h and a. (b) what is the probability that a randomly chosen young driver is an honor student and is involved in an accident? (c) find the percent of honor students who are involved in accidents.

Answer 1

The probabilities given in terms of events h and a are: P(h) = 10%, P(a) = 20%, and P(a|h) = 5%. The probability that a randomly chosen young driver is an honor student and is involved in an accident is 0.5%. The percent of honor students who are involved in accidents is 5%.

Step-by-step explanation:

(a) The probabilities given in terms of events h and a are:

1. P(h) = 10% (10% of young drivers are honor students)
2. P(a) = 20% (20% of young drivers are involved in accidents each year)
3. P(a|h) = 5% (5% of honor students are involved in accidents)

(b) To find the probability that a randomly chosen young driver is an honor student and is involved in an accident, we multiply the probabilities of the two events:

P(h ∩ a) = P(a|h) * P(h) = 5% * 10% = 0.05 * 0.1 = 0.005 = 0.5%

(c) To find the percent of honor students who are involved in accidents, we divide the probability of the intersection of the two events by the probability of being an honor student:

Percent of honor students involved in accidents = (P(h ∩ a) / P(h)) * 100 = (0.005 / 0.1) * 100 = 0.05 * 100 = 5%.