Prof. Edwin Romeijn
ESI 6321 Applied Probability Methods For Engineers
Homework 1 - Solutions
ESI 6321 APPLIED PROBABILITY METHODS FOR ENGINEERS
Homework 1 – Spring 2008
(a) A total of 8 outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT.
(b) P(HHT) = 1/8.
(c) P(First two tosses are heads) = 2/8.
(d) P(Two heads in a row) = 3/8.
(a) According to the table above, the prime time slot would yield the highest expected
net profit, $112,000.
(b) The company should buy the morning and the prime time slots, with a total
expected contribution to earnings of $152,000.
Let S1 denote the lamp comes from first shipment, S2 denote the lamp comes from
second shipment, and D denote the lamp is defective. We want to compare P(S1 | D)
to P(S2 | D). We have P(S1) = 100/150 = 2/3, P(S2) = 50/150 = 1/3, P(D | S1) = 0.04,