A fair coin is tossed five times with all tosses being independent. Compute the probabilty that the coin comes up heads at least three times in a row.

Question

Math team. It is hard but i dont know how to figure it out. Someone plase help understand it. Don't just give me tge answer.

Answer 1

There are only 3 ways you can get 3 heads in a row:

HHHxx, xHHHx, and xxHHH where the xx represents either H or T.

Each of these 3 configurations can happen in 4 ways depending on the 2 x's.

This means that there are 12 ways to get at least 3 heads in a row.

In total there are 32 ways in which a coin can land .

Therefore, the probability requested is 12/32 =3/8