Answer:
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%
