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Today Puzzle #631

Puzzle No. 631– Thursday 12 December

My niece is representing her school in a TV game show. She needs a partner and she's asked me to join her. For the game there are twenty doors, all empty except for one of the doors behind which is a top-of-the range phone. We're both asked to choose a door. Then the host, one by one, reveals 16 empty doors. With four doors left, we're given the opportunity to change our minds. Straight away my niece says we should both swap doors. I don't quite understand, but I follow her lead. By how much has my niece increased our chances of winning?

Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of the Royal Institution

Click here for the answer

9 times

To start with we had a 2 in 20 chance of winning.

There is an 18 in 20 chance that the phone is in a door we didn't choose.

If it's not in one of our doors, then the host has concentrated the phone into one of the two other doors. If we both swap then we have that 18/20 chance of winning. So, we've increased our chances 9-fold

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