Question

Q2. 90% of flights depart on time. 80% of flights arrive on time. 75% of flights depart on time and arrive on time. Are the events, departing on time and arriving on time, independent?

Answer 1

Events departing on time and arriving on time are NOT independent.

Step-by-step explanation:

If two events A and B are independent, then

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

Here

A = flights depart on time

B = flights arrive on time

P(A) = 0.90

P(B) = 0.80

If A and B are independent, then

P(A and B) = P(A) * P(B) = 0.9 * 0.8 = 0.72

Since

the observed value of P(A and B) is 0.75,

assuming that there are no observation errors, we conclude that the two events A and B are not independent.