SOLUTION: Two fair coins were tossed and it is known that at least one was a head. Find the probability that they were both heads.

When two fair coins are tossed, the space of events consists of four elements


HH   (*)
HT   (*)
TH   (*)
TT


Of them, the sub-space consisting of three elements, marked (*) in the list, is the sub-space  "at least one is head".


In this sub-space of three elements, only one HH is "two heads", or, equivalently, "both heads".


Therefore, the conditional probability under the question is  .