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Wise Betting Enigma

Story: Jill offered Jack the following bet: she said she would toss 3 pennies in the air, and if they fell all heads or all tails she would give him $1. If they fell any other way, he had to give her 50 cents.

Enigma: Should Jack accept?

Solution: NO! It would be very unwise of Jack to accept the bet. To find the chances that the 3 coins will fall alike or not alike, consider all the possible ways that the 3 coins can fall, as follows:
1:HHH
2:HHT
3:HTH
4:HTT
5:THH
6:THT
7:TTH
8:TTT
Each of the 8 possibilities is equally likely to occur. Note that only 2 of them show all the coins alike. this means that the chances of all 3 coins being alike are 2 out of 8, or one quarter. There are 6 ways that the coins can fall without being all alike. Therefore the chances that this will happen are three-quarters.

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