You are going to meet a friend at the airport. Your experience tells you that the plane is late 70% of the time when it rains, but is late only 20% of the time when it does not rain. What is the probability that the plane will be late?

0.4

Step-by-step explanation:

Probability of rain = P (R)

Probability of late plane = P (L)

So, the probability of no rain = P (R')

Breaking it down

If it rains, 40% chance, P (R) = 0.4

That the plane would be late if it rains = 70% * 40%, that is, P (R n L) = 0.7 * 0.4 = 0.28, 28% of the total chance.

That the plane would be on time if it rains = 30% * 40%, that is, P (R n L') = 0.3 * 0.4 = 0.12, 12% of the total chance.

If it doesn't rain, 60% chance, P (R') = 1 - P (R) = 1 - 0.4 = 0.6

That the plane would be late if it doesn't rain = 20% * 60%, that is, P (R n L') = 0.2 * 0.6 = 0.12, 12% of the total chance.

That the plane would be on time if it doesn't rain = 80% * 60%, that is, P (R' n L') = 0.8 * 0.6 = 0.48, 48% of the total chance.

So, probability that the plane would be late = P (L) = P (R n L) + P (R' n L) = 0.28 + 0.12 = 0.4 = 40%