Any help would be appericated. I'm going to see if I can figure out 19.) by myself right now, so I'll update it if I figure it out before someone answers incase anyone else is having trouble with a question like this.
UPDATE - I did them both, I don't know if they are done correctly though.
21.) Interpret the following probability statement into words. Is this an example of mutually exclusive events? Explain.
P(A∪B) = P(A) + P(B) − P(A∩B)
EDIT - The probability of A union B is equivalent to the difference of probability of product of probability of A and probability of B and, the probability of A intersetion B.
A company has two factories that manufacture light bulbs. Suppose that 55% of the light bulbs are
manufactured in factory A and 45% come from factory B. In factory A 0.7% of the bulbs are defective and in factory B 0.3% of the bulbs are defective. Suppose a defective light bulb is discovered. What is the probability that the defective bulb came from factory B?
EDIT - P(B | defective) = P(B & defective) / P(defective) = 0.135/0.52 = 0.2596 or 25.96%
I think that is correct?
Let us suppose that 100000 total bulbs are manufactured by both factories...55000 by A and 45000 by B
So.....the number of defects are 55000 * .007 + 45000 * .003 = 520
So....out of the 520 defects........45000*.003 = 135 come from B
So.....the probability that a defective bulb comes from B given that we have a defective bulb is just
135 / 520 = .2596
Just as you found !!!