Challenging Questions

Mathematics – Compulsory Part

Learning Unit: More about probability

Question M0-16-04

Two people, Ben and Ron, take turns rolling a fair six-sided die. Ben rolls first, and Ron rolls second. The first player to roll a one (1 dot) wins the game.

1. Determine the probabilities of Ben winning in the first, second, and third rounds of the game. Please express your answers as fractions.
2. Determine the probabilities of Ron winning in the first, second, and third rounds of the game. Please express your answers as fractions.
3. Show that Ben has a higher probability of winning the game than Ron.
4. Show that the sum of the probabilities of Ben winning and Ron winning is 1.

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