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# Probability ..

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Senior Manager
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Probability .. [#permalink]

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10 May 2009, 21:27
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The probability is 1/2 that a coin will turn out to be tails on any given toss. A coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses.
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Re: Probability .. [#permalink]

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11 May 2009, 19:03
typhoidX wrote:
tenaman10 wrote:
The probability is 1/2 that a coin will turn out to be tails on any given toss. A coin is tossed 5 times. What is the probability of getting at least three heads on consecutive tosses.

I think this is a really stupid way to do this, but I suck at probabilities, so...

Here are the orders in which at least 3 consecutive heads can appear:
HHHTT, THHHT, TTHHH, HHHHT, THHHH, HHHTH, HTHHH, HHHHH
So there is a total of 8 variants that satisfies this condition.

The total number of ways for five tosses is 2^5 = 32 (I think?)

So the probability would be 8/32 or 1/4?? I guess...?

Agree with you... good job.

total possibilitites = 2^5 = 32

no of 3 consecutive heads = 3 + 2= 5
no of 4 consecutive heads = 2
no of 5 consecutive heads = 1
total = 8

prob = 8/32 = 1/4
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Re: Probability .. [#permalink]

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15 May 2009, 13:53
is there any mathematical way of solving this.

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Re: Probability .. [#permalink]

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15 May 2009, 13:56
Yes there is and it's pretty straight forward.

HHHTT
HHHHT
HHHHH
THHHT
THHHH
TTHHH

Those are the 6 ways we can get 3 consecutive heads.

How many different outcomes to the flips are there? $$2^5=32$$.

Hence Pr(>= 3 consecutive heads) [m]= 6/32 = 3/16.
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Re: Probability ..   [#permalink] 15 May 2009, 13:56
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# Probability ..

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