1. ## Probability problem set

I'm having alot of trouble with these homework problems and how to solve them.

Bob sets two alarm clocks (battery−powered) to be sure he arises for his Monday 8:00 A.M. accounting exam. There is a 73 percent chance that either clock will wake Bob. What is the probability that Bob will oversleep? If Bob had three clocks, would he have a 99 percent chance of waking up?

Half of a set of the parts are manufactured by machine A and half by machine B. Two percent of all the parts are defective. Four percent of the parts manufactured on machine A are defective. Find the probability that a part was manufactured on machine A, given that the part is defective.

I really appreciate if anyone could help me with these

2. I'll give you a couple of hints:

Question 1:

I am assuming both locks A and B have the probability of 73% each of waking bob up, that is, p = 0.73
for clock A and p=0.73 for clock B. so the probability of clock A not waking Bob up would be (1-0.73 = 0.27).Same for clock B..
Can you now find the probability that both clocks wont wake bob up?

Question 2:
Probability that A is defective: $P(A) = 0.5$

Probability that the parts are defective: $P(D) = 0.02$

Probability that part is defective given it was manufactured on A: $P(D|A) = 0.04$

you have to find the probability that the part was manufactured on A given that it is defective, that is, : $P(A|D)$

Find P(A|D) using CONDITIONAL PROBABILITY