Math HELP!?

Question

A cellular phone manufacturer randomly selects 5 of every 50 phones from the assembly line and tests them. If at least 4 out of 5 pass inspection, the batch of 50 is considered acceptable. Fine the probability that a batch of 50 phones is considered acceptable given the following additional information:

1. the batch of 50 phones contains 2 defectives
2. the batch contains no defectives

for number 1, I got .21
number 2 I got .311
Is this right??

Answer 1

I find the best way to look at problems like this is to come from the other direction.
1) What is the probability of getting both defective phones? (both need to be pulled in order for the batch to be unacceptable).
First off, there are 50-choose-5 possible selections of 5 phones = 2118760.
There are 5-choose-2 ways of pulling the 2 defective phones = 10.
Of the remaining 3 slots, there are 48-choose-3 selections of phones to pull = 17296.
So the probability is ways of getting bad phones = 10*17296 / ways of getting phones = 2118760.
So chance is 4/49. That is the chance of the batch being unacceptable - so acceptable chance is 45/49=.918367
Note: I would consider this to be an impressively difficult probability problem. I may have done it incorrectly.
2) There are no defective phones, so there is no way that the batch could be considered acceptable. This means that the probability of getting an acceptable batch is 1.

Answer 2

Sorry, no, I am sure you are wrong.

With 1, the batch will only be rejected if the two defectives are in the sample of 5. What is the probability of that - quite small.

With 2, there can never be any defectives in the sample. So there is 100% probabilty the batch will be considered acceptable.