Question

A fair coin is tossed three times.what is the probability that at least two heads will occur given that at most two heads have occurred?

Answer 1

There are eight possible outcomes: HHH,HHT,HTH,HTT,THH,THT,TTH,TTT. Seven (all but HHH) have at most two heads. Three of these seven (HHT,HTH,THH) have at least two heads. The probability is therefore 3 in 7 or about 42.86%.