Probability problem on light bulbs

Forum Index GMAT Math

New MBA Student Life Forum: Ask your questions to current MBA students from Harvard, Stanford, Wharton, Kellogg and Haas

Post new topic   Reply to topic

r_walid
Rising GMAT Star



Joined: 21 Jan 2009
Posts: 43

Thanks given: 0
Thanked 1 times in 1 posts
Topic: Probability problem on light bulbs
PostThu Oct 29, 2009 11:38 am Reply with quote
There are 10 light bulbs and fewer than half are defective. If n is the number of defective light bulbs, what is the value of n if the probability that one of the bulbs will be defective and the other will not be = 7/15?
Back to top
View user's profile Send private message
ayashlaha
Just gettin' started!



Joined: 25 Oct 2009
Posts: 7

Thanks given: 0
Thanked 2 times in 2 posts
PostThu Oct 29, 2009 5:06 pm Reply with quote
Please post the answer tot he question. I have some ideas but i'm getting multiple answers.
Back to top
View user's profile Send private message
crackthetest
Just gettin' started!



Joined: 16 Feb 2009
Posts: 28

Thanks given: 6
Thanked 3 times in 3 posts
PostThu Oct 29, 2009 6:09 pm Reply with quote
Is n = 4? Pl. post OA.
Back to top
View user's profile Send private message
life is a test
Really wants to Beat The GMAT!



Joined: 02 Mar 2009
Posts: 136

Thanks given: 4
Thanked 8 times in 8 posts
PostThu Oct 29, 2009 7:26 pm Reply with quote
n=3?

probability of getting one defective and one non defective bulb = (prob of getting first one defective and second one non-defective) + (probability of getting the first one non-defective and the second one defective)
--> (n/10 * 10-n/9) + (10-n /10 * n/9) = 7/15
--> factorize to solve for n to give n = 7 or 3, since n <5 hence n =3
Back to top
View user's profile Send private message
jzdchou
Rising GMAT Star



Joined: 05 Mar 2009
Posts: 32

Thanks given: 0
Thanked 0 times in 0 posts
Location: NYC

Test Date: 3/7/09
Target GMAT Score: 700
GMAT Score: 640
PostMon Nov 02, 2009 10:56 am Reply with quote
should the question be asking which n gives you 7/15?

10C2 = 45 given the total number of ways to pick 2 bulbs out of 10

6G4D = 24 pairs of 1G and 1D -> 24/45 = 8/15
7G3D = 21 pairs of 1G and 1D -> 21/45 = 7/15
8G2D = 16 pairs of 1G and 1D -> 16/45
9G1D = 9 pairs of 1G and 1D -> 9/45

confused
Back to top
View user's profile Send private message
David_IBaspirant
Just gettin' started!



Joined: 02 Nov 2009
Posts: 1

Thanks given: 0
Thanked 0 times in 0 posts
PostMon Nov 02, 2009 8:44 pm Reply with quote
Here's the question cut and pasted:

There are 10 light bulbs and fewer than half are defective. If n is the number of defective light bulbs, what is the value of n if the probability that one of the bulbs will be defective and the other will not be = 7/15?

Ok, with that said, this is a difficult
simultaneous probability question.

The question is giving you two scenarios. The first one, you pick a defective light bulb and THEN a non-defective light bulb. Consider this P(A) * P(B). In the second scenario, you pick a good light bulb on the first try and THEN a defective light bulb. Consider this P(B) * P(A).

Now that you have the two equations, you will need to ADD them together. Why? Because either/OR will work, and whenever you see the word "or", think: addition. (When you see the word "and", think multiply)

Let's set up the full equation:

[P(A) * P(B)] + [P(B) * P(A)]


Let's try n=3.

(3/10 * 7/9) + (7/10 * 3/9)
= 21/90 + 21/90
= 42/90
= 7/15

Why is the denominator a "9" in the second piece of each multiplication? Well, if you take 1 light bulb out of a batch of 10, then on the second try, how many light bulbs do you have to choose from? Right, you have 9. Consider this a probability without replacement simultaneous equation.

If you like this post, I am only a student. I took the Veritas GMAT prep course and gotta vouch for them. They review combinatorics and probabilities in depth. Email me for info. I'm testing this Friday for the GMAT, and ready to roll. Best![i][/b]
Back to top
View user's profile Send private message
Display posts from previous:   

Post new topic   Reply to topic All times are GMT - 8 Hours
Page 1 of 1