Question

The probability that a driver receives a speeding ticket is 0.7. And the probability that a driver is under 25 years old is 0.8. The probability that a driver is under 25 years old is 0.9 given that he has received a speeding ticket

A) find the probability that the driver received a speeding ticket and is under 25 years old

B) what is the probability that the driver is under 25 years old or received a speeding ticket

Answer 1

Let, A be an event that a driver receives a speeding ticket.

B be an event that a driver is under 25 years old.

P(A) = 0.7

P(B) = 0.8

P(B | A) = 0.9

A) We want to find, P(A and B)

P(B | A) = P(A and B) / P(A)

=> P(A and B) = P(B | A) * P(A)

=> P(A and B) = 0.9 * 0.7

=> P(A and B) = 0.63

Therefore, the probability that the driver received a speeding ticket and is under 25 years old is 0.63

B) We want to find, P(A or B)

P(A or B) = P(A) + P(B) - P(A and B)

=> P(A or B) = 0.7 + 0.8 - 0.63

=> P(A or B) = 0.87

Therefore, the probability that the driver is under 25 years old or received a speeding ticket is 0.87