# probability that 2 heads do not occur consecutively when a fair coin is tossed 10 times?

A sequence of n > 2 coin tosses has no consecutive heads if, and only if:

- It begins with a tail, and is followed by n−1 tosses with no consecutive heads; or
- It begins with a head, then a tail, and is followed by n−2 tosses with no consecutive heads.

cindybrown wrote: 9 . A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?

cindybrown wrote: 9 . A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?

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Alternatively, we could argue that the 1st coin has probability 1/2 to come up heads or tails, the 2nd coin has probability 1/2 to come up heads or tails, and so on for the 3rd and 4th coins, so that the probability for any one particular sequence of heads and tails is just (1/2)x(1/2) x (1/2)x(1/2)=(1/16).

Since the probability to flip a head is the same as the probability to flip a tail, the probability of outcome (i) must be equal to the probability of outcome (ii). So both must be equal to 1/2.

So Pr(3) = 1- Pr(1) – Pr(2) = 1- (1/2)^N – (1/2)^N

= 1 – power(1/2,N-1)

I consider that someone would only continue flipping if he/she has not flipped two heads in a row. That is, is not in the done state.

That is, for any toss level N, it wrong to assume that number of nodes is equal to 2^N. It will be strictly smaller as of level N = 3.

Anyway, after 3-4 levels drawn, one should see a pattern, that is, the number of tails, or initial state nodes (is), at a level N is equal to the number of is’s I had at level N-1 + the number of is’s I had at level N-2. We can thus write:

## References:

http://www.beatthegmat.com/a-fair-coin-is-tossed-t80355.html

http://doubtnut.com/question-answer/a-fair-coin-is-tossed-10-times-then-the-probability-that-two-heads-do-not-occur-consecutively-is-7-6-36468

http://www.pas.rochester.edu/~stte/phy104-F00/notes-2.html

http://www.glassdoor.com/Interview/What-the-probability-of-getting-2-consecutive-heads-in-a-total-of-N-tosses-I-found-this-one-pretty-hard-and-I-didn-t-figur-QTN_285314.htm

http://www.newsnation.in/fact-check/news/fact-check-has-reserve-bank-of-india-issued-rs-1000-coin-244954.html