1. A microchip company has two machines that produce the chips. Machine I produces 65% of the chips and Machine II produces 35% of the chips. 5% of Machine I chips are defective and 15% of Machine II chips are defective.
a) A chip is selected at random, what is the probability that it is from Machine I and is defective?
b) A chip is selected at random, what is the probability that it is defective?
c) If a chip is known that came from Machine II, what is the probability that it is defective?
A chip is selected at random and known to be defective, what is the probability that it came from Machine I?
2. The probabilities that Jack and Jill can solve a homework problem are 0.6 and 0.4 respectively. The probability that both of them can solve a homework problem is 0.24.
a) Determine if the chances of Jack and Jill can solve the homework problem are independent to each other or mutually exclusive (disjoint) to each other? Prove and explain your conclusion.
b) Find the probability that Jack will and Jill won't solve the problem.
c) Find the probability that exactly one of them will solve the problem.
d) Find the probability that neither of them will solve the problem. (5 points)