20. The three marbles
Two persons,
A and
B, compete to see who can roll a marble closest to a “target.”
Both are equally skilled but
A is allowed only one roll while
B is allowed two.
Assuming there is no chance of a tie, what is the probability that
A will win?
One way to figure it is that
A should have 1 chance in 3 of winning, since he has one roll and
B has two, and they are equally skilled.
But another way to figure it is that
A should only have 1 chance in 4 of winning, since either of
B’s rolls has a 50-50 chance of beating
A’s roll, and
B has two independent chances of doing this.
Which answer do you think is right, and why?
From Ernest Adams, A Primer of Probability Logic. Originally from Eugene Northrop, Riddles in Mathematics.