Long Division

Discrete Mathematics Level 4

Parliament is \( \dfrac{1}{3} \) Conservative members, who are incapable of changing their minds about anything, and \( \dfrac{2}{3} \) Labour members who change their minds completely at random (with probability \( 50\% \)) between successive votes on the same issue.

A randomly chosen member is observed to have voted twice in succession the same way. What is the probability that he will vote in the same way next time?

Note: Votes in the UK parliament are called divisions, hence the title

Image Credit: Catherine Bebbington used under a free licence.

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