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Math question

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Math question  [#permalink]

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New post 27 Jan 2011, 08:09
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Hi,

Can you please solve this?

"If the coin is tossed 5 times, what is the probability that at least 3 out of 5 times it will show heads?"

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Re: Math question  [#permalink]

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New post Updated on: 27 Jan 2011, 09:58
petrifiedbutstanding wrote:
Hi,

Can you please solve this?

"If the coin is tossed 5 times, what is the probability that at least 3 out of 5 times it will show heads?"


If a coin is tossed 5 times, at each toss there are 2 possibilities H or T. So there are in all 2^5 = 32 possible outcomes e.g. HHHHH, HHTHH, HTTTH etc

Of these, we want those in which we get at least 3 heads.
So let us try and find the cases where we get 3/4/5 heads.

3 heads - we have to arrange HHHTT in as many different ways as possible e.g. HHTHT, TTHHH etc.
No of ways of arranging 5 letters 3 of which are same and 2 of which are same = 5!/3!2! = 10 ways

4 heads - Arrangements will be HHHHT, HHTHH etc
No of ways of arranging 5 letters 4 of which are same = 5!/4! = 5 ways

5 heads - there is only one such arrangement HHHHH

Hence probability of getting 3/4/5 heads = No of ways of getting 3/4/5 heads/Total no of ways = 16/32 = 1/2

Note: We don't really need to solve when we need 3/4/5 heads because we can have 0/1/2/3/4/5 heads and correspondingly 5/4/3/2/1/0 tails. Since the cases are symmetrical, half of them will have 0/1/2 heads(and 5/4/3 tails) and the other half will have 3/4/5 heads (and 2/1/0 tails)

BTW, I think you need to post PS questions in the Quant - PS forum.
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Originally posted by VeritasKarishma on 27 Jan 2011, 08:55.
Last edited by VeritasKarishma on 27 Jan 2011, 09:58, edited 1 time in total.
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Re: Math question  [#permalink]

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New post 27 Jan 2011, 09:09
I am trying to help you but I am far to be a GMAT guru so it would be nice if someone more qualified could verify what I am saying.

How many ways are there to do 3 heads ou of 5? Is this the same to ask you how many words can be done with 3*h and 2*t

5!/2!3!= 5*4*3*2/2*3*2*

10* the number (of the probability to have any of the situation on the 5 shots=1/2^5) 2*2*2*2*2=32

10/32 or 1/16 is it possible?
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Re: Math question  [#permalink]

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New post 27 Jan 2011, 09:10
Hi Karishma,

Are you not invalidating the choice of getting more that 3 heads , you are only considering hthth, why not hhhht and hhhhh that is 4 heads and 5 heads.

I feel answer should be 1/2


VeritasPrepKarishma wrote:
petrifiedbutstanding wrote:
Hi,

Can you please solve this?

"If the coin is tossed 5 times, what is the probability that at least 3 out of 5 times it will show heads?"


If a coin is tossed 5 times, at each toss there are 2 possibilities H or T. So there are in all 2^5 = 32 possible outcomes e.g. HHHHH, HHTHH, HTTTH etc

Of these, we want those in which we get 3 heads.
i.e. we have to arrange HHHTT in as many different ways as possible e.g. HHTHT, TTHHH etc.
No of ways of arranging 5 letters 3 of which are same and 2 of which are same = 5!/3!2! = 10 ways

Hence probability of getting 3 heads = No of ways of getting 3 heads/Total no of ways = 10/32 = 5/16

BTW, I think you need to post PS questions in the Quant - PS forum.
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Re: Math question  [#permalink]

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New post 27 Jan 2011, 09:15
Suddenly your feeling makes me feel the same, I remember a section in the veritas prep books, to be careful with coins as the chance to have: H-h-t-t-t is actually the same as to have t-t-t-h-h...
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Re: Math question  [#permalink]

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New post 27 Jan 2011, 09:17
However I believe an Veritas GMAT instructor knows what he says :-)
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Re: Math question  [#permalink]

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New post 27 Jan 2011, 09:51
Duke007 wrote:
However I believe an Veritas GMAT instructor knows what he says :-)


Sorry, the GMAT instructor did not read the question properly... skipped 'at least'... that should be a lesson!!!
I will edit the solution given above..
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Re: Math question  [#permalink]

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New post 27 Jan 2011, 11:34
VeritasPrepKarishma wrote:
Duke007 wrote:
However I believe an Veritas GMAT instructor knows what he says :-)


Sorry, the GMAT instructor did not read the question properly... skipped 'at least'... that should be a lesson!!!
I will edit the solution given above..


Thanks for the solution.

But can you explain the post script note again? I don't understand it.
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Re: Math question  [#permalink]

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New post 28 Jan 2011, 18:16
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petrifiedbutstanding wrote:
But can you explain the post script note again? I don't understand it.


Sure.
When you toss a coin 5 times, possibilities range from HHHHH, HHHHT, HHHTH...... TTTTT.
The number of heads can be 0/1/2/3/4/5.

In these 32 arrangements, each arrangement will have either 3/4/5 Heads or 3/4/5 Tails (When there are 0/1/2 heads, the number of tails will be 5/4/3 respectively).
Since Heads and Tails are equal in status i.e. their probability of appearing is the same, whatever is the probability of 3/4/5 heads, same will be the probability of 3/4/5 tails. Together they account for probability 1 since every arrangement will have either 3/4/5 heads or 3/4/5 tails. So probability of each will be 1/2.
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Re: Math question  [#permalink]

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New post 28 Jan 2011, 23:23
VeritasPrepKarishma wrote:

Sure.
When you toss a coin 5 times, possibilities range from HHHHH, HHHHT, HHHTH...... TTTTT.
The number of heads can be 0/1/2/3/4/5.

In these 32 arrangements, each arrangement will have either 3/4/5 Heads or 3/4/5 Tails (When there are 0/1/2 heads, the number of tails will be 5/4/3 respectively).
Since Heads and Tails are equal in status i.e. their probability of appearing is the same, whatever is the probability of 3/4/5 heads, same will be the probability of 3/4/5 tails. Together they account for probability 1 since every arrangement will have either 3/4/5 heads or 3/4/5 tails. So probability of each will be 1/2.


Ah. I see. So essentially, what you're saying is, just by looking at the problem and doing some shrewd analysis, the solution is quite straightforward.

Thanks. This is a great approach.
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Re: Math question  [#permalink]

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New post 29 Jan 2011, 11:44
Karishma- u have a skill of teaching... thanks. +1 again.

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Re: Math question   [#permalink] 29 Jan 2011, 11:44

Math question

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