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# A gambler has a 1 in 5 chance of winning his first bet, and

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CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
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Kudos [?]: 387 [0], given: 4

A gambler has a 1 in 5 chance of winning his first bet, and [#permalink]  23 Nov 2007, 13:41
A gambler has a 1 in 5 chance of winning his first bet, and a 1 in 7 chance of winning his second bet, and 1 in 7 chance of winning his third bet. What is his chance of winning exactly one of the bets if they are independent?
Senior Manager
Joined: 06 Aug 2007
Posts: 368
Followers: 1

Kudos [?]: 23 [0], given: 0

Re: gambling probability [#permalink]  23 Nov 2007, 14:01
bmwhype2 wrote:
A gambler has a 1 in 5 chance of winning his first bet, and a 1 in 7 chance of winning his second bet, and 1 in 7 chance of winning his third bet. What is his chance of winning exactly one of the bets if they are independent?

I think there are 2 possible answers:

1. 36/245

2. 24/245
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [0], given: 359

Expert's post
12/35

p=1/5*6/7*6/7+4/5*1/7*6/7+4/5*6/7*1/7=(6*6+2*4*6)/(5*7*7)=

=6*14/(5*7*7)=12/35
SVP
Joined: 28 Dec 2005
Posts: 1579
Followers: 2

Kudos [?]: 91 [0], given: 2

walker wrote:
12/35

p=1/5*6/7*6/7+4/5*1/7*6/7+4/5*6/7*1/7=(6*6+2*4*6)/(5*7*7)=

=6*14/(5*7*7)=12/35

bingo. i didnt reduce, so i ended up with 84/245
CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 387 [0], given: 4

WL or LW

1/5*6/7 = 6/35
4/5*1/7 = 4/35

6/35 + 4/35= 10/35 = 2/7
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [0], given: 359

Expert's post
bmwhype2 wrote:
WL or LW

1/5*6/7 = 6/35
4/5*1/7 = 4/35

6/35 + 4/35= 10/35 = 2/7

it is suitable for two bets but we have three ones...
CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 387 [0], given: 4

walker wrote:
bmwhype2 wrote:
WL or LW

1/5*6/7 = 6/35
4/5*1/7 = 4/35

6/35 + 4/35= 10/35 = 2/7

it is suitable for two bets but we have three ones...

sorry. i was looking at a different version of this problem.

should be 84/245, using the same method.
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