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?

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

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.

hopefull this will you!

the business rule that governs the relationship is one-to-many as there are multiple customers for each agent.