Question

1. (20pts) Your favorite pizza place is extremely slow with deliveries. If you remember to order an hour early, there is a 75% chance that the pizza will arrive by the start of your favorite TV show. If you do not remember, there is a 20% chance that the pizza will arrive by the start of the show. Because you are so distracted by a cool probability puzzle, you estimate that there is only a 90% chance that you will remember to order early. (a) What is the probability that the pizza is on time? (b) If the pizza is on time, what is the probability that you forgot to order early? (Let T be the event that pizza arrives on time and R be the event that you remembered to order pizza early)

Answer 1

solubon: 1) P(I) = 0.75 PI I J = 0.20 P(R) = 0.9 a) P(T) = P(OR) + PITOR) = Plu). PIP) + PIEC). PIRC) = 0.75 X0.9 +0.20 x (1-0.9) 0.695 bp/R = PIRRT) = P(c). PIRS PIT) PIT) - 0.200.1 0.695 = [0, 0288