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5 coins are tossed. If two of them show heads, then the

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Manager
Joined: 14 Dec 2004
Posts: 119
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5 coins are tossed. If two of them show heads, then the [#permalink]  31 Mar 2005, 17:36
5 coins are tossed. If two of them show heads, then the probability that all 5 coins show head is

a. 1/32
b. 1/10
c. 1/26
d. 1/13
e. none of the above
Director
Joined: 18 Feb 2005
Posts: 674
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Kudos [?]: 2 [0], given: 0

the 2 coins prob is 1

rest 3 coins prob is (1/2)^3 = 1/8
Manager
Joined: 14 Dec 2004
Posts: 119
Followers: 1

Kudos [?]: 10 [0], given: 0

OA on this is C. (1/26)
Director
Joined: 27 Dec 2004
Posts: 908
Followers: 1

Kudos [?]: 19 [0], given: 0

I got A...what am i doing wrong agian
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

Total number of combinations:
0H 5T - 1 way
1H 4T - 5 ways
2H 3T - 10 ways
3H 2T - 10 ways
4H 1T - 5 ways
5H 0T - 1 way

Total # of combinations = 32 ways

Number of combinations that all are heads, is only 1: HHHHH

So Probability = 1/32
SVP
Joined: 03 Jan 2005
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Re: coin [#permalink]  01 Apr 2005, 09:06
cloaked_vessel wrote:
5 coins are tossed. If two of them show heads, then the probability that all 5 coins show head is

a. 1/32
b. 1/10
c. 1/26
d. 1/13
e. none of the above

Total outcome:2^5=32
Outcome of at least two of them show heads:
Probability=1/26
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Last edited by HongHu on 01 Apr 2005, 09:50, edited 1 time in total.
Manager
Joined: 14 Dec 2004
Posts: 57
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Re: coin [#permalink]  01 Apr 2005, 09:38
HongHu wrote:
cloaked_vessel wrote:
5 coins are tossed. If two of them show heads, then the probability that all 5 coins show head is

a. 1/32
b. 1/10
c. 1/26
d. 1/13
e. none of the above

Total outcome:2^5=32
Outcome of at least two of them show heads:
Probability=1/26

why do we have to subtract 5 from 32.
SVP
Joined: 03 Jan 2005
Posts: 2250
Followers: 13

Kudos [?]: 216 [0], given: 0

Sorry, the 1 is for 0 head, and the 5 is for 1 head. I'll edit the post to make it clearer.

Basically the question implies that two of them are heads but the other three can also be heads. So we need to know what probability is for getting at least two heads. It'll be total minus the cases where we only get one head, and where we get no heads.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

VP
Joined: 18 Nov 2004
Posts: 1442
Followers: 2

Kudos [?]: 20 [0], given: 0

Re: coin [#permalink]  01 Apr 2005, 11:04
HongHu wrote:
cloaked_vessel wrote:
5 coins are tossed. If two of them show heads, then the probability that all 5 coins show head is

a. 1/32
b. 1/10
c. 1/26
d. 1/13
e. none of the above

Total outcome:2^5=32
Outcome of at least two of them show heads:
Probability=1/26

Honghu, how do u know that "If two of them show heads" means "atleast 2 heads"...thx
SVP
Joined: 03 Jan 2005
Posts: 2250
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Kudos [?]: 216 [0], given: 0

There are two explanations for this sentence "two of the coins show heads". One is that exactly two coins are heads. The other is at least two are heads. The next sentence askes "What probability is all coins show heads". You know that means in additional to the two heads, the other coins may show heads too. In other word there would be two or more heads, or at least two heads.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

VP
Joined: 13 Jun 2004
Posts: 1122
Location: London, UK
Schools: Tuck'08
Followers: 7

Kudos [?]: 31 [0], given: 0

Sorry guys but I don't get this one. the question is :

5 coins are tossed. If two of them show heads, then the probability that all 5 coins show head is ?

We already know that 2 of them showed heads, no ? In my opnion it should be 1/8 becasue there are still 3 toss to make and the events are independant : (1/2)^3

What's wrong with 1/8 ?
SVP
Joined: 03 Jan 2005
Posts: 2250
Followers: 13

Kudos [?]: 216 [0], given: 0

Because it didn't say that the first two throw were heads. It just said that two out of five are heads and we don't know the others.
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

VP
Joined: 13 Jun 2004
Posts: 1122
Location: London, UK
Schools: Tuck'08
Followers: 7

Kudos [?]: 31 [0], given: 0

Thanks Hong Hu, I got it now
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