5. Two factories supply light bulbs to UConn buildings, 99% of the bulbs from fa
ID: 3277350 • Letter: 5
Question
5. Two factories supply light bulbs to UConn buildings, 99% of the bulbs from factory X have a lifetime of 5000 hours, whereas 95% of the bulbs from factory Y function for 5000 hours. Factory X supplies 60% of the total of bulbs. (a) What is the probability that a purchased bulb w actually work for 5000 hours? (b) Given that a light bulb works 5000 hours, what is the probability that it was delivered by factory (c) Given that a light bulb work fails before the 5000 hours, what is the probability that it was Y? delivered by factory X?Explanation / Answer
(a) Probability that the purchased bulb is from factory X = 60% = 0.6
Probability that a bulb from factory X will work for 5000 hours = 0.99
=> Probability that a purchased bulb from factory X will work for 5000 hours = 0.6 * 0.99 = 0.594
Probability that a purchased bulb is from factory Y = 40% = 0.4
Probability that a bulb from factory Y will work for 5000 hours = 0.95
=> Probability that a purchased bulb from factory Y will work for 5000 hours = 0.4 * 0.95 = 0.38
=> Probability that a purchased bulb will work for 5000 hours = 0.594 + 0.38 = 0.974 or 97.4%.
(b) Probability that the bulb which worked for 5000 hours was purchased from factory Y
= 0.38 / 0.974
= 0.39 or 39%.
(c) Probability that a light bulb purchased from factory X fails before 5000 hours = 0.6 * 0.01 = 0.006
Probability that a light bulb purchased from factory Y fails before 5000 hours = 0.4 * 0.05 = 0.02
=> Probability that a light bulb which failed before 5000 hours was from factory X = 0.006 / 0.026
= 0.2308
or 23.08%.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.