Notes from the underground
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Updated 2 December 2023
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.