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A fair coin is tossed $10$ times, the tosses being indipendent of each other. I have to find the probability that 3rd, 4th and 5th tosses are identical.

I have no idea how to calculate. please help.

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1 Answer

up vote 2 down vote accepted

Hint: Two possibilities (i) three heads and (ii) three tails. What is the probability of $3$ consecutive heads? Of three consecutive tails? Add.

The fact that there were $10$ tosses is irrelevant. And the fact that $3$, $4$, and $5$ are next to each other s irrelevant. We would have the same answer to "what is the probability the the $2$nd, $5$th, and $10$th tosses are identical?"

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probability of three consequtive head is $1/8$, and same for the tails, hence $1/4$? –  Bunuelian Trick Oct 4 '12 at 8:58
    
Yes, that is correct.${}{}{}{}{}$ –  André Nicolas Oct 4 '12 at 9:00
    
thank you very much Andre –  Bunuelian Trick Oct 4 '12 at 9:02
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Alternately, we don't care what the $3$rd toss was. The probabilty the $4$th matched it is $(1/2)$, and the probability the $5$th matched that is $(1/2)$, for a probability of $(1/2)(1/2)$. Simpler! But it is useful to get accustomed to dividing things into cases. –  André Nicolas Oct 4 '12 at 9:04
    
I understand, thanks a lot.. –  Bunuelian Trick Oct 4 '12 at 9:10
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