Question: The Prime minister is trying to decide whether to call an election. He decides to phone a random telephone number, and ask the advice of the person who answers the phone. He is duty bound to follow their advice.

Two fifths of phone calls are answered by men, two fifths are answered by women, and one fifth are unanswered. Men will tell him to call an election with probability two-thirds, women will tell him to call an election with probability one-quarter, if the call is not answered then he calls an election if the (fair) coin in his pocket lands heads when he spins it.

The Prime Minister follows this procedure. What is the probability that there is an election?

Given that there is no election, what is the probability that the phone call went unanswered.

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