Question

80% of an airline's flights depart on-time and 20% do not. Of those that depart on-time, 95% arrive on-time. Of those that depart late, 10% arrive on-time. What is the chance of someone taking a flight that will arrive on-time?

Answer 1

0.78

Explanation:

given that 80% of an airline's flights depart on-time and 20% do not.

Of those that depart on-time, 95% arrive on-time. Of those that depart late, 10% arrive on-time

Let A be the event that flight departs on time.

Now A and A' are mutually exclusive and exhaustive

Let B be the event the flight arrives on time

Using total probability calculation we have

the chance of someone taking a flight that will arrive on-time

= P(B)

=
`P(A)+P(A'B)\\= 0.80(0.95) +0.20(0.10)\\= 0.76+0.02\\=0.78`