Problem B

Let the Game Begin!

Parvinder and Carlos are each rolling a standard six-sided die, with numbers \(1\) to \(6\) on its sides, to see who gets to go first in their game. The person who rolls the lower number gets to go first. If they tie, they roll again.

What is the theoretical probability that Parvinder will roll a number lower than Carlos on their first roll? Hint: What are the possibilities for Carlosâ€™ roll if Parvinder rolls a \(1\)? a \(2\)? a \(3\)?

What is the theoretical probability that Parvinder will roll a number greater than Carlos on their first roll?

Is this a fair way to determine who goes first?

**Theme:** Data Management