# If the first 3 flips of a fair coin are tails, what is the probability that the next flip will be heads?

A person decides to flip a coin until it lands on heads.

Part 1:

What is the probability that the first time it lands on heads is on the 4th flip (that is, it lands on 3 tails before it lands on heads for the first time).

I understand this question. Using the geometric distribution, I solve for P(x=$4$):

P(Heads) = $0.5$
P(Tails) = $0.5$

P(X=$4$) = $0.5^3$ x $0.5^1$ = $0.5^4$ = $0.0625$

Part 2:

If their first $3$ flips are tails, what is the probability that the next flip will be heads?

I'm not sure how where to start? To me, this sounds exactly like Part 1. Any help is appreciated.

Thanks

• As long as the tosses are independent of each other no matter if the last $1$ billion tosses were tail when the probability of the next toss being head is asked. It is $1/2$ Oct 3, 2014 at 21:11

Since any toss does not affect or influence the outcome of any other toss, the probability of getting a heads is the same old $1/2$.