Probability that 3 heads will occur on 6 flips of fair coin given that head occurs on fifth as well as sixth toss.

Question

Suppose an experiment consists of tossing a fair coin until three heads occur. What is the probability that experiment ends after exactly six flips of the coin with a head on the fifth toss as well as sixth?

Now I know how to solve for the case; when I have to find probability of three heads to occur in 6 independent tosses of fair coin. I use the binomial distribution with $n$=6 , $x$=3 and get result $P(x=3)$ = 5/16
What confuses me is the last condition of getting head on fifth and sixth trial. How do I proceed?

Answer 1

Hint:

To get the experiment to end with three heads after exactly six flips of the coin with a head on the fifth toss as well as sixth, you need

• exactly one of the first four to be heads
• the fifth to be heads
• the sixth to be heads