A pair of dice is rolled. Find the probability of rolling
30
(a) a sum not more than 10 ,
(b) a sum not less than 4 .
(c) a sum between 3 and 8 (exclusive).
(Simplify your answer.)
How many ways can two dice be rolled such that their sum is not more than 10 ?
33
(Simplify your answer.)
The probability of rolling a sum not more than 10 is $\frac{11}{12}$.
(Type an integer or a simplified fraction.)
(b) How many ways can two dice be rolled such that their sum is not less than 4 ?
33
(Simplify your answer.)
The probability of rolling a sum not less than 4 is $\square$.
(Type an integer or a simplified fraction.)
Answer
Final Answer: The number of ways two dice can be rolled such that their sum is not more than 10 is \(\boxed{33}\). The probability of rolling a sum not more than 10 is \(\boxed{\frac{33}{36}}\).
Step 1 ：When two dice are rolled, the total possible outcomes are 36. This is because each die has 6 faces, and so the total outcomes are \(6 \times 6 = 36\).
Step 2 ：We are asked to find the outcomes where the sum of the numbers on the two dice is not more than 10. After calculating, we find that there are 33 such outcomes.
Step 3 ：Thus, the probability of rolling a sum not more than 10 is the ratio of the desired outcomes to the total outcomes. This is calculated as \(\frac{33}{36}\).
Step 4 ：Final Answer: The number of ways two dice can be rolled such that their sum is not more than 10 is \(\boxed{33}\). The probability of rolling a sum not more than 10 is \(\boxed{\frac{33}{36}}\).
