Problem #3?
 

Box 1 contains 1000 bulbs of which 10% are defective. Box 2 contains 2000 bulbs of which 5% are defective. Two bulbs are picked from a randomly selected box.

(a) Find the probability that both bulbs are defective.
(b) Assuming that both are defective, find the probability that they came from box 1.


*Not the easiest problem, but very doable for y'all.

(a) If it is selected at random then that means that there is a 7.5% chance that one would be defective. Sqaure that, and you get .5625% chance that they are both defective.

(b) 1/4?

It matters not whether you win or lose; what matters is whether I win or lose.

(a) Nope. Too large. How did you get the 7.5%? It's not correct by the way.
(b) Nope...

Two bulbs are picked from a randomly selected box, so it has a 50% chance of being box 1 with a 10% defective chance, and 50% chance of being box 2 with 5% chance of being defective. If they're picked at random, would you not take the average of the 5% and the 10%?

Well, if it was box 1, the first bulb has a 10% chance of being defective, but for a second consecutive bulb to be picked out of box 1, it is a 99/999 times that 1/10. Take that hint and go with it!

It matters not whether you win or lose; what matters is whether I win or lose.

Ok, let me take another stab at answer a. ~.5599%?

A defective bulb from box one is probabilty 100/1000 --> 1/10
A defective bulb from box two is probability 100/2000 --> 1/20

a) 200/3000 --> 2/30
b) Oh God, I hate these questions. Gotta draw bloody diagrams. Gimme a few min.
Ah fuck it. Can't be bothered.

Go with:

a) 2/30
b) 1/30 ???

No to all. It was actually a lot tougher a problem than I initially thought.

Bleh...I dislike math...

Well, not really I just don't like it.

Chance of defective for the first pick is 200/3000 = 6.6667%
Chance of defective for second pick is 199/2999 = 6.6355%

Chance of that happening is .4424%.

Chance the first was from box one: 100/200 = 50%.
Chance the second was from box one as well: 99/199 = 49.75%

Chance of both being from box one is 24.87%.

Unless you have to factor in the total number in each box... In which case... Fuck it. I get of in 5 minutes.

ITS IN PLAIN SIGHT!!! they were both picked from the same box!! if they were picked from box 1 then...

A) 15 percent chance they are both defective!
B) DUH 50% chance!!!

Holy God I hate math. :P

Doh on the wording.

I suppose "Two bulbs are picked from a randomly selected box." would imply that they were both picked from one box.

That means b) is 50%.

Now, however, the method of solving a chances.

50% chance of box 1 and percentage of 2 defective there is 100/1000 * 99/999 = .990990% (repeating) chance.

50% chance of box 2 and percentage of 2 defective there is 100/2000 * 99/1999 =
.2476238% chance.

Add half the first percent to half the second percent, and there's your answer.

.6193% chance of having 2 defective bulbs. (That is, if you're assuming they're both picked from one box.)