Question

A fair coin is flipped repeatedly. What is the probability the fourth tail comes before the sixth head?

Answer 1

So, the question is indirectly asking us the probability of getting 5 heads and 3 tails in 8 flips and then a tail in 9th flip.

Probability of getting a head in a flip = 1/2

Probability of getting a tail in a flip = 1/2

Now,

Let the Probability of getting 5 heads in 8 flips be P(5H8),

Now, after this in 9th flip we need a tail whose probability will be 1/2.

Now, probability that the fourth tail comes before the sixth head will be = Probability of getting 5 heads in 8 flips × Probability of getting a tail in 9th flip

Probability that the fourth tail comes before the sixth head = 0.21875 × 0.5 = 0.109375 or 10.9375%