Answer to Question #124835 in Statistics and Probability for Yasini

Question

Under good weather conditions, 80% of flights arrive in time. During a bad weather only 30% of flights arrive on time. Tomorrow the chance of good weather is 60% what is the probability that your flights arrive in time?

Answer 1

P(on time|good weather) = 0.80

P(on time|bad weather) = 0.30

P(good weather) = 0.60 ==> P(bad weather) = 0.40

Then

P(on time) = P(on time AND good weather) + P(on time AND bad weather)

=P(on time|good weather)*P(good weather) + P(on time|bad weather) * P(bad weather)

=0.80*0.60 + 0.30*0.40 = 0.60, the probability that your flight will arrive on time.