Today Puzzle #681
Puzzle No. 681– Friday 21 February 2020
Justin realised Mishal tricked him in their die vs coin game, so he changed the rules of the game so that the person who gets a 4 first wins. Mishal throws a fair six-sided die, while Justin tosses a fair coin 6 times and needs precisely 4 heads in order to win in his turn. Who has the more chances to win the game?
Today’s #PuzzleForToday has been set by Dr Nicos Georgiou, a senior mathematics lecturer from the University of Sussex.
Click here for the answer
In this case, Justin has more chances. Mishal’s overall chance of winning in a single turn is 1/6 ~ 16.7%. Justin needs 4 heads out of 6; each coin has a probability ½ of landing heads, but the four heads can happen for any 4 of the 6 coins. There are 15 different ways to have 4 heads and two tales (e.g. HHHHTT, HTHTHH, and so on), so overall his chance of winning in a turn is 15x1/64~ 23%.
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