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# Five coins are tossed. what is the probability that exactly

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Intern
Joined: 05 Aug 2008
Posts: 13
Five coins are tossed. what is the probability that exactly [#permalink]

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19 Aug 2008, 08:29
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Five coins are tossed. what is the probability that exactly 3 coins land tail side up?
Senior Manager
Joined: 06 Apr 2008
Posts: 401

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19 Aug 2008, 08:43
Five coins are tossed. what is the probability that exactly 3 coins land tail side up?

Total combinations = 2^5 = 32

No. of fav combinations = 5! / 3! * 2! = 10

Prob. = 10/32 = 5/16
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Joined: 30 Apr 2008
Posts: 1855
Location: Oklahoma City
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19 Aug 2008, 09:03
I agree with this solution up to the point where we find out how many favorable combinations there are of the 3 selected being tails, but you have to subtract out the instances where the 2 remaining coins are not heads because if one of the remaining 2 is a Tails, then that is not "exactly three coins landing tails up".

nmohindru wrote:
Five coins are tossed. what is the probability that exactly 3 coins land tail side up?

Total combinations = 2^5 = 32

No. of fav combinations = 5! / 3! * 2! = 10

Prob. = 10/32 = 5/16

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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a\$\$.

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Senior Manager
Joined: 06 Apr 2008
Posts: 401

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19 Aug 2008, 09:16
jallenmorris wrote:
I agree with this solution up to the point where we find out how many favorable combinations there are of the 3 selected being tails, but you have to subtract out the instances where the 2 remaining coins are not heads because if one of the remaining 2 is a Tails, then that is not "exactly three coins landing tails up".

nmohindru wrote:
Five coins are tossed. what is the probability that exactly 3 coins land tail side up?

Total combinations = 2^5 = 32

No. of fav combinations = 5! / 3! * 2! = 10

Prob. = 10/32 = 5/16

For exactly 3 tails , it means rest 2 are heads.

Now 3 tails and 2 heads can be arranged in 5 slots in 5!/2!*3! ways = 10

Therefore Prob = 5/16.

Nowhere in my solution am I considering 4Tails or 5 Tails.
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Joined: 30 Apr 2008
Posts: 1855
Location: Oklahoma City
Schools: Hard Knocks

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19 Aug 2008, 09:18
I see what you're saying. The question didn't seem like it could be that simple. I tend to overcomplicate Combination questions.
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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a\$\$.

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Joined: 19 Mar 2008
Posts: 350

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19 Aug 2008, 09:43
Five coins are tossed. what is the probability that exactly 3 coins land tail side up?

5C3*(1/2)^5
= (5*4/2)/32
= 10/32
= 5 /16
Re: probability   [#permalink] 19 Aug 2008, 09:43
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# Five coins are tossed. what is the probability that exactly

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