A problem from the October 1964 issue of Eureka, the journal of the Cambridge University Mathematical Society:

My friend tosses two coins and covers them with his hand. ‘Is there at least one “tail”?’ I ask. He affirms this (a).

Just then he accidentally knocks one of them to the floor (b). On finding the dropped coin under the table, we discover it to be a ‘tail’ (c).

‘That is all right,’ he says, ‘because it was a “tail” to start with.’ (d).

At each point (a), (b), (c) and (d) of this episode I calculated what, to the best of my knowledge, was the probability that both coins showed ‘tails’ at the time. What were these probabilities?