Probability -Difficult

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gmatrant: Master | Next Rank: 500 Posts; Posts: 416; Joined: Wed Oct 03, 2007 9:08 amFollowed by: 1 member; Thanked: 10 times

by gmatrant » Sat Oct 13, 2007 9:41 pm

A and B pick up a card at random from a well shuffled pack of cards, one after the other, replacing it every time till one of them gets a heart. A begins the game , then the probability that the game ends with B is

1) 3/7 2)4/7 3)3/4 4)1/4

Ans : [spoiler]1)[/spoiler]

Solution: I couldnt get to the answer , but this is what I tried. Where could I be going wrong?

p(A does not pick heart) = 3/4
p(B picks heart) = 1/4

p(of B winning is) = (3/4)* (1/4)= 3/16.
But thats no where near the answer.

Please correct me where I am going wrong.

Thanks

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Source: Beat The GMAT — Problem Solving | Sat Oct 13, 2007 9:41 pm

agni_mba: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Mon Aug 13, 2007 3:04 am; Location: india

by agni_mba » Sun Oct 14, 2007 2:56 pm

The trick is in understanding that this game may never end. The probability of B winning will be summation of probs. associated winning in the first run, second run, third run and so and so forth.

P(B)1st run = (3/4)*1/4 = 3/16
P(B)2nd run = [No result in 1st run]* (3/16) = [9/16]*3/16
P(B)3rd run = [no result in 1st AND 2nd run]*3/16 = [9/16*9/16]*3/16
and so and so forth...

when you sum this infinite GP up you will get the answer.

cheers

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gmatrant: Master | Next Rank: 500 Posts; Posts: 416; Joined: Wed Oct 03, 2007 9:08 amFollowed by: 1 member; Thanked: 10 times

by gmatrant » Sun Oct 14, 2007 7:29 pm

agni_mba wrote:The trick is in understanding that this game may never end. The probability of B winning will be summation of probs. associated winning in the first run, second run, third run and so and so forth.

P(B)1st run = (3/4)*1/4 = 3/16
P(B)2nd run = [No result in 1st run]* (3/16) = [9/16]*3/16
P(B)3rd run = [no result in 1st AND 2nd run]*3/16 = [9/16*9/16]*3/16
and so and so forth...

when you sum this infinite GP up you will get the answer.

cheers

Oh yes your are right.. great .thanks for the solution

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jangojess: Master | Next Rank: 500 Posts; Posts: 175; Joined: Mon Jul 02, 2007 12:01 pmFollowed by: 1 member; Thanked: 15 times

by jangojess » Sun Oct 14, 2007 10:18 pm

simply superb man.....where did u get this pblm from???

Trying hard!!!

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