The Game
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
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?
HintTheir dad is a very smart person.
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Answer
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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Comments
tpg76
May 03, 2008
 Not too hard, and these are always fun. Thanks.
Good explanation of the answer. 
LavaIcee
May 04, 2008
 I thought it was hard, but it was fun... 
Zozo_The_Zo
May 16, 2008
 i guessed and i got it right!!!! i feel so smart 
Shadows
Nov 16, 2008
 The hint made it easy to guess, but I actually figured out the calculations! Good one! 
Lord_Hawk
Jan 04, 2009
 A fun diversion from the daily routine. Simple, but gets your brain working a bit.
Thanks 
sylvalant
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 ! 
opqpop
Jan 26, 2010
 Too easy if you know anything about probability. 
ron93
Feb 26, 2015
 liked this one, this question is a good review to probability. I got the formulation correct somehow and got the answer 
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