View Full Version : Problem #3?
Titusfied
2004-12-02, 08:49 PM
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.
Demosthenes
2004-12-02, 09:14 PM
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?
Shining Knights
2004-12-02, 09:16 PM
It matters not whether you win or lose; what matters is whether I win or lose.
Titusfied
2004-12-02, 09:20 PM
(a) Nope. Too large. How did you get the 7.5%? It's not correct by the way.
(b) Nope...
Demosthenes
2004-12-02, 09:45 PM
(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%?
Titusfied
2004-12-02, 09:49 PM
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!
Shining Knights
2004-12-02, 09:59 PM
It matters not whether you win or lose; what matters is whether I win or lose.
Demosthenes
2004-12-02, 10:09 PM
Ok, let me take another stab at answer a. ~.5599%?
Lenny
2004-12-03, 01:56 PM
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 ???
Titusfied
2004-12-03, 02:02 PM
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.
Medieval Bob
2004-12-03, 04:55 PM
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.
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.
Draco2003
2004-12-04, 03:04 PM
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!!!
Jamesadin
2004-12-04, 05:52 PM
Holy God I hate math. :P
Medieval Bob
2004-12-05, 08:50 AM
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.)
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