Last year, Warren Buffett promised to pay one billion dollars to the person that
ID: 3172836 • Letter: L
Question
Last year, Warren Buffett promised to pay one billion dollars to the person that got the NCAA Basketball 64 team bracket completely correct. This year, he has offered one million dollars per year for life to the person that gets the bracket completely correct. Warren Buffett can afford to do this because of his wealth (if you have never heard of Warren Buffett, google his name). Someone with no knowledge of basketball would have to guess on the outcome of each game and therefore would have a 50% chance of selecting the correct winning team. Someone who is knowledgeable and has lets say a 70% chance of correctly predicting who will win any one game, would do better in getting the bracket just right. What is the probability for each of these two individuals (the one with no knowledge and the one with knowledge) to win the million for life? Remember that in principle, each game is independent of all others. Whatever happens in one does not affect what happens in some other game.
Explanation / Answer
To win the million for life, individual has to correctly predict winners of 64 games
If the probability of correctly prediciting the winner of basket ball game = p
then probability of correctly predicitng the winner of two basket ball games = probability of correctly prediciting the winner of first basket ball game x probability of correctly prediciting the winner of second basket ball game =pxp = p2
Similarly probability of correctly predicting the winner of three basket ball games =pxpxp = p3
Probability of correctly predicting the winner of 64 basket ball games = p64
Some with no knowledge of basket ball would guess on outcome of basketball game = 50%
Someone who is Knowledgeable of basket ball would guess on outcome of basketball game =70%
Probability of a person with no knowledge correctly predicting the winner of a basketball game PNK = 50/100 =0.5
Probability of a person with knowledge correctly predicting the winner of a basketball game PK =70/100 = 0.7
Proabaility of a person with no knowledge of basketball correctly predicting the winner of 64 basket ball games = PNK64=0.564 = 0.00000000000000000005421010862
Proabaility of a person with knowledge of basketball correctly predicting the winner of 64 basket ball games = PK64=0.764 =0.000000000121976048763583
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