Two fair six-sided dice are rolled independently. Amir says: “The possible sums are 2 to 12. There a

Question

Two fair six-sided dice are rolled independently.
Amir says:

“The possible sums are 2 to 12. There are 11 sums, so each sum has probability $\frac1{11}$.”

Explain his mistake. Calculate the probabilities of a sum of $2$ and a sum of $7$.

Two games are then offered:

- Game A : Win if the sum is at least $10$.
- Game B : Win if both dice show the same number.

Accepted Answer

(a) Sums are not equally likely: $\frac1{36}$, $\frac16$; (b) Equal: $\frac16$ each

Probability