The Envelopes
There are 10 envelopes in a hat. One of the envelopes has a check for $10,000. There are two people who are each going to grab an envelope out of the hat. First, Mike (Person 1) is going to grab an envelope. Then, Ike (Person 2) will grab an envelope. Who has a better chance of getting the $10,000?
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1 solution
Could you average all of the possible events for Ike? For instance, you could average all possible outcomes for Ike numerically by doing this: 1 0 9 0 + 9 1 + 9 1 + 9 1 + 9 1 + 9 1 + 9 1 + 9 1 + 9 1 + 9 1 to get the same answer: 10%.
MIKE has a 10% chance of grabbing the envelope, because there are 10 envelopes. IKE , first has a 90% chance of MIKE not grabbing it. Then, he has 1/9 of a 90% chance, because there are 9 envelopes left. That gives IKE a 10% chance, the same as MIKE 's. They have an equal chance.