Probability -Difficult

Expert replies

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

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

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

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!!!

Featured schoolRound 2 closes Jan 7, 2027 54 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review