Question

In a certain city, 5 percent of all drivers have expired licenses, 10 percent have an unpaid parking ticket, and 1 percent have both an expired license and an unpaid parking ticket. Are these events independent?

Answer 1

The events are not independent.

Explanation:

Events A and B are independent if the occurrence of one does not effect the occurrence of the other.

If events A and B are independent then:

`P(A\cap B)=P(A)* P(B)`

Denote the events as follows:

E = a driver has an expired license.

U = a driver has an unpaid parking ticket.

The information provided is:

P (E) = 0.05

P (U) = 0.10

P (E ∩ U) = 0.01

If events E and U are independent then:

P (E ∩ U) = P (E) × P (U)

Compute the value of P (E) × P (U) as follows:

`P (E) * P (U)=0.05*0.10=0.005`

So P (E ∩ U) ≠ P (E) × P (U).

Thus, events E and U are not independent.