Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
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?"

share|cite|improve this answer
probability of three consequtive head is $1/8$, and same for the tails, hence $1/4$? – Un Chien Andalou Oct 4 '12 at 8:58
Yes, that is correct.${}{}{}{}{}$ – André Nicolas Oct 4 '12 at 9:00
thank you very much Andre – Un Chien Andalou Oct 4 '12 at 9:02
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.. – Un Chien Andalou Oct 4 '12 at 9:10

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.