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## The Game

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Fun: (2.71) Difficulty: (2.23) Category: Probability Submitted By: fro92

Mike and James are arguing over who gets the last cookie in the jar, so their dad decides to create a game to settle their dispute. First, Mike flips a coin twice, and each time James calls heads or tails in the air. If James gets both calls right, he gets the last cookie. If not, Mike picks a number between one and six and then rolls a die. If he gets the number right, he gets the last cookie. If not, James picks two numbers between one and five, then spins a spinner with numbers one through five on it. If the spinner lands on one of James' two numbers, he gets the last cookie. If not, Mike does.

Who is more likely to win the last cookie, Mike or James? And what is the probability that person wins it?

Believe it or not, both Mike and James have a 1/2 chance of winning.

James wins if:
-he calls both coin flips right = 1/2 x 1/2 = 1/4
OR
-he does not call both coin flips right, Mike does not call the die roll correctly, and he guesses the number on the spinner right = 3/4 x 5/6 x 2/5 = 30/120 = 1/4

1/4 + 1/4 = 1/2

Mike wins if:
-James does not call both coin flips right and he calls the die roll correctly = 3/4 x 1/6 = 3/24 = 1/8
OR
-James does not call both coin flips right, he does not call the die roll correctly, and Mike does not guess the number on the spinner right = 3/4 x 5/6 x 3/5 = 45/120 = 3/8

1/8 + 3/8 = 1/2

Of course, dad could have just flipped a coin.

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 Posted by tpg76 on May 03, 2008 Not too hard, and these are always fun. Thanks. Good explanation of the answer. Posted by LavaIcee on May 04, 2008 I thought it was hard, but it was fun... Posted by Zozo_The_Zo on May 16, 2008 i guessed and i got it right!!!! i feel so smart Posted by Shadows on Nov 16, 2008 The hint made it easy to guess, but I actually figured out the calculations! Good one! Posted by Lord_Hawk on Jan 04, 2009 A fun diversion from the daily routine. Simple, but gets your brain working a bit. Thanks Posted by sylvalant on Jan 10, 2009 My dad likes to waste time too. Next time he needs to make a decision I'll tell him to flip a coin ! Posted by opqpop on Jan 26, 2010 Too easy if you know anything about probability.