Question

Suppose you flip a fair coin 10 times. What is the probability of the last two flips both being heads if you know that the first eight flips were heads?

Answer 1

As the coin is a fair coin, the results of all tosses are independent of each other. That means, first eight tosses do not change the occurrence of the last two tosses.

Now the probability of getting head for a fair coin is 1/2. Hence the probability of the last two flips both being heads is (1/2)*(1/2) = 1/4.

You can alternatively calculate the answer by listing the possible outcomes of the last two flips:

Outcomes are: HH, HT, TH & TT

Hence, the probability of the last two flips both being heads (HH) is 1/4.