Today Puzzle #681
Puzzle No. 681鈥� 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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