Problem B

Gamer!

Geoff plays a game using two standard six-sided dice: a black one and a white one. To win the game, Geoff must roll the dice and have the numbers on the two top faces sum to \(11\).

What is the probability that he rolls a \(7\) with just the black die?

What is the theoretical probability that he rolls a \(1\) on the black die and a \(6\) on the white die?

If he rolls both dice and calculates the sum of the numbers on the two top faces, what sum(s) have the lowest theoretical probability of being rolled?

What is the theoretical probability of rolling both dice and the sum of the numbers on the two top faces is \(7\)?

What is the theoretical probability of rolling both dice and the sum of the numbers on the two top faces is \(11\)?

Roll two dice thirty-six times and keep track of the number of times the numbers on the two top faces sum to \(11\). What was your empirical probability of rolling a sum of \(11\)?

Share your results in part (f) with your classmates. How many had their empirical probability of rolling a sum of \(11\) equal the theoretical probability of rolling a sum of \(11\)?

**Themes: **Data Management, Number Sense