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The Bet

Joan offered Jim the following bet:
She would toss 3 pennies in the air,
and if they fell all heads or all tails she would give him $1.
If the coins fell with any other combination, he had to give her 50 cents.
Should Jim take this bet?

It would not be very wise for Jim to take the bet. 
Consider all the possible ways that the 3 coins can fall :

 HHH   HHT   HTH    HTT   THH   THT   TTH   TTT

Each of the 8 possibilities is equally likely to occur. 
Only 2 of the cases show all the coins alike. 
Therefore, the chances that all 3 coins will be alike are 2 out of 8.
The chances the coins will not be all alike are 6 out of 8. 
Therefore Joan would pay Jim $1, once out of every 4 tosses,
and Jim would pay Joan 50 cents, for 3 out of every 4 tosses. 
Joan would win more money than Jim on these terms.