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# 5 people flip a coin.

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Intern
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5 people flip a coin. [#permalink]  19 Oct 2004, 13:42
Hey All,

This is a pretty simple one but i just want to make sure.

5 people flip a coin... what is the probability that there will be one odd-man out (i.e. 4 heads, 1 tail; 4 tails, 1 head).

Isn't it 1/32 ?
Manager
Joined: 16 May 2004
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I think the answer is 4C1* (1/2)^5 *2 = 1/4

4C1 because the 1 head can appear any where meaning
it could be one of the combinations

HTTTT
THTTT
TTHTT so on

and since the outcome could also have 1T and 4 H

it is twice
GMAT Club Legend
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I would say 5C4 * 2 * (1/2)^5 = 5/16
5C4 because you have 5C4 ways of picking 4 heads out of 5 tosses. Same goes for 4 tails thus you multiply by 2.
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Paul

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Re: 5 people flip a coin. [#permalink]  20 Oct 2004, 00:26
zfreshjive wrote:
Hey All,

This is a pretty simple one but i just want to make sure.

5 people flip a coin... what is the probability that there will be one odd-man out (i.e. 4 heads, 1 tail; 4 tails, 1 head).

Isn't it 1/32 ?

Paul is correct -
To get 4 haeds and 1 tail -
(1/2) * (1/2) * (1/2) * (1/2) * (1/2) * 5 = 5/32
Same way, to get 4 tails and 1 head -
5/32
So,
probability = 5/32 + 5/32 = 5/16

cheers,
Dharmin
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Better Solution : Total outcome : 2^5 = 32

Favourable outcomes (4H 1T and 4T IH) = 5!/(4! * 1!) + 5!/(4! * 1!)
= 10

Intern
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the probability of 1 person out of 5 (1/5) getting 4H,1T(1/2*1/2*1/2*1/2 *1/2)or 4T,1H is
1/5 * 1/2*1/2 *1/2 * 1/2 * 1/2 + 1/5* 1/2* 1/2* 1/2* 1/2 * 1/2 =
1/5(1/32 + 1/32)=1/5*1/16 = 1/80
CIO
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agree with 5/16. My way has no probability formula at all:

First, the denominator - the total number of possibilities when flipping a coin 5 times = 2^5 = 32.

Then, the numerator. How many ways can a heads come up just once or a tails come up just once? There can't be that many! Let's just lay them out:

H T T T T
T H T T T
T T H T T
T T T H T
T T T T H

That's 5 with heads once, so it must also be 5 with tails once. Since we're talking about different people, each ordering is different, so they all count. So we've got 10 total ways.

So probability: 10/32 = 5/16
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Thanks [#permalink]  20 Oct 2004, 11:53
Thanks, everyone.
Thanks   [#permalink] 20 Oct 2004, 11:53
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