Question

5. A coin is to be tossed until a head appears twice. What is the sample space for this experiment? If the coin is fair, what is the probability that it will be tossed exactly four times?

Answer 1

Sample space = S = {(HH), (THH), (HTHH), (TTHH), (HTTHH), (THTHH), ...}

Where HH denotes two heads, THH a tails then two heads, HTHH denotes a heads, a tails, then two heads etc.

There will be 2^4 = 16 total possible outcomes in 4 flips.

Of those only two (HTHH and TTHH) will satisfy the given restraint (stop when two heads in a row appear) at four flips exactly. (HHHH wouldn't satisfy this since we'd stop at two flips, TTTH wouldn't since we still have to keep flipping etc.).

Assuming the coin is fair then this leads to a probability of 2/16 = 1/8.