Question

Leah is flying from Boston to Denver with a connection in Chicago. The probability her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Chicago is 0.95, but if the first flight is delayed, the probability that the luggage will make it is only 0.65.

A) Are the first flight leaving on time and the luggage making the connection independent events? Explain.
B) What is the probability that her luggage arrives in Denver with her?

Answer 1

(A) The two events are Not Independent.

(B) The probability that Leah's luggage arrives in Denver is 0.695.

Explanation:

Let F = Leah's first flight leaves on time and C = Leah's luggage will make the connecting flight.

Given:

P (F) = 0.15, P (C|F) = 0.95 and P (C|F') = 0.65

Here F' represents the events that Leash's first flight was not on time.

(A)

The events F and C are not independent.

For the luggage to make the connecting flight Leah's first flight must be on time.

As it is provided that the probability that the the luggage will make the connecting flight provided that the first flight is delayed is 0.65, i.e. there 0.35 probability that the luggage will not make the connecting flight.

Thus, implying that the two events F and C are dependent.

(B)

Compute the probability that Leah's luggage arrives in Denver as follows:

P (D) = P (C|F) × P (F) + P (C|F') × P (F')

`= (0.95*0.15)+(0.65* (1-0.15))\\=0.695`

Thus, the probability that Leah's luggage arrives in Denver is 0.695.