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Probability of repeated trials

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Probability of repeated trials [#permalink] New post 08 Aug 2006, 16:51
guys I am looking for a formula to solve this problem:

Coin tossed 4 times. What is probability that atleast 3 out of 4 tosses will come up heads? (answer is 5/16)

kaplan did it by writing out all combinations of H&Ts. I know that's going to be a PITA on exam day for me, so I'd rather have a neat formula handy.

Why doesn't this formula work for me?

.....................N!
BDF = ------------------ * p^M * (1 — p)^N — M
.............(N — M)! * M!

BDF = the binomial distribution probability;
p = the individual probability of the phenomenon (p = 0.5 to get heads in coin tossing);
M = the exact number of successes
N = the number of trials

Thx!

Last edited by Nsentra on 08 Aug 2006, 16:55, edited 1 time in total.
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 [#permalink] New post 08 Aug 2006, 16:54
I have the same problem! How in the heck are you going to right it all out on exam day without wasting 2-3 minutes on a problem?
I have never seen it asked like that on GMAT prep..
so I wouldln't worry too too much..
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 [#permalink] New post 08 Aug 2006, 16:58
jamesrwright3 wrote:
I have the same problem! How in the heck are you going to right it all out on exam day without wasting 2-3 minutes on a problem?
I have never seen it asked like that on GMAT prep..
so I wouldln't worry too too much..

:writer
I appreciate Kaplan for putting some stuff for me in baby terms, but sometimes by not explaining everything behind the answer they are preventing me from seeing the real math behind the solution
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 [#permalink] New post 08 Aug 2006, 17:06
Why am not getting 5/16? In fact, I am getting 1-5/16=11/16... Confused

Prob(of at least 3 heads)= 1 - Prob(0 or 1 heads)

Pron(0 or 1 heads) = ?

Total number of possible combinationsL 2^4=16

0 heads: 1 combination (when all tails)
1 head, 3 tails: 4 combinations

Prob(0 or 1) = (1+4)/16 = 5/16

Prob(3 or more)=1-5/16=11/16

???
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 [#permalink] New post 08 Aug 2006, 17:19
v1rok wrote:
Why am not getting 5/16? In fact, I am getting 1-5/16=11/16... Confused

Prob(of at least 3 heads)= 1 - Prob(0 or 1 heads)

Pron(0 or 1 heads) = ?

Total number of possible combinationsL 2^4=16

0 heads: 1 combination (when all tails)
1 head, 3 tails: 4 combinations

Prob(0 or 1) = (1+4)/16 = 5/16

Prob(3 or more)=1-5/16=11/16

???


They are saying there are 5 possible outcomes with alteast 3 heads in 4 tosses

hhht
hhth
hthh
thhh
hhhh

the word 'atleast' is prob. why my probability formula is not working out

so 5/16

Last edited by Nsentra on 08 Aug 2006, 17:20, edited 1 time in total.
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 [#permalink] New post 08 Aug 2006, 17:19
Nevermind, I found where I got derailed:

P(3 or more)= 1 - P(0,1,or2)

He-he, looks like I need some rest...
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 [#permalink] New post 08 Aug 2006, 17:22
v1rok wrote:
Nevermind, I found where I got derailed:

P(3 or more)= 1 - P(0,1,or2)

He-he, looks like I need some rest...


Is this the only way to solve this problem? Write out all possible outcomes? there is no algebraic formula?
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 [#permalink] New post 08 Aug 2006, 17:24
Exactly, nissan! I was working too quickly (trying to fit in those 2 minutes!) and accidently skipped one case...

Anyway, you don't have to write down all possible combinations of heads and tails.

You just need to remember that 2^4 is total number of combinations (=16)
and then count only those cases where we have eaither 4 heads (1 such case) or 3 heads (4 cases). So,

Prob=5/16
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 [#permalink] New post 08 Aug 2006, 17:27
v1rok wrote:
Exactly, nissan! I was working too quickly (trying to fit in those 2 minutes!) and accidently skipped one case...



I know for a fact that is what is going to happen to me on a test. Thanks for giving another thought on how to do this though. :-D
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 [#permalink] New post 08 Aug 2006, 17:31
Nsentra wrote:
v1rok wrote:
Exactly, nissan! I was working too quickly (trying to fit in those 2 minutes!) and accidently skipped one case...



I know for a fact that is what is going to happen to me on a test. Thanks for giving another thought on how to do this though. :-D


Cheer up! That's exactly why you are here, isn't it. A little bit of practicing and you will get confident enough so that none of the tricks GMAT trows at you would make you blink...
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 [#permalink] New post 08 Aug 2006, 22:57
Prob of getting exactly three heads = 4C3 * (1/2)^3 * (1/2)^1 = 4/16

Prob of getting exactly 4 heads = 4C4 * (1/2)^4 = 1/16

Total prob = 1/16 + 4/16 = 5/16
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Last edited by ps_dahiya on 11 Aug 2006, 10:18, edited 1 time in total.
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 [#permalink] New post 09 Aug 2006, 09:58
ps_dahiya wrote:
Prob of getting exactly three heads = 4C3 * (1/2)^3 * (1/2)^1 = 4/16

Prob of getting exactly 4 heads = 4C4 * (1/2)^4 = 1/16

Total prob = 1/16 + 4/16 = 5/16


Perfect! Thanks! (great quote too)
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 [#permalink] New post 10 Aug 2006, 13:07
ps_dahiya,

could you explain the formula that you used. seems simple
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 [#permalink] New post 10 Aug 2006, 13:15
rkatl wrote:
ps_dahiya,

could you explain the formula that you used. seems simple

Its is explained here by the math goddess HongHu:

http://www.gmatclub.com/phpbb/viewtopic.php?t=14706
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 [#permalink] New post 11 Aug 2006, 09:21
PS_dahiya,
There is a typo in your reply. Please don't mistake me. I know you are so good. Just to help others to understand ....

Probability of winning head or tail in tossing coin is 1/2

your answer says 1/3 instead of 1/2

Prob of getting exactly three heads = 4C3 * (1/2)^3 * (1/3)^1 = 4/16

Prob of getting exactly 4 heads = 4C4 * (1/2)^4 = 1/16

Total prob = 1/16 + 4/16 = 5/16.

BTW, your link about probability is too good.
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 [#permalink] New post 11 Aug 2006, 10:19
How I approached the problem:

16 possible outcomes altogether (4*4)

Getting at least 3:
Getting all 4-
4C4 = 1

Getting 3 out of 4:
4C3 = 4

4+1 = 5

5/16 [/u]
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 [#permalink] New post 11 Aug 2006, 10:19
baski6 wrote:
PS_dahiya,
There is a typo in your reply. Please don't mistake me. I know you are so good. Just to help others to understand ....

Probability of winning head or tail in tossing coin is 1/2

your answer says 1/3 instead of 1/2

Prob of getting exactly three heads = 4C3 * (1/2)^3 * (1/3)^1 = 4/16

Prob of getting exactly 4 heads = 4C4 * (1/2)^4 = 1/16

Total prob = 1/16 + 4/16 = 5/16.

BTW, your link about probability is too good.

Thanks buddy. I have corrected the error.
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  [#permalink] 11 Aug 2006, 10:19
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