A pair of dice is rolled. Find the probability of rolling
a) a sum not more than 9 ,
b) a sum not less than 3 .
c) a sum between 5 and 9 (exclusive).
a) The probability of rolling a sum not more than 9 is $\frac{5}{6}$.
(Type an integer or a simplified fraction.)
b) The probability of rolling a sum not less than 3 is (Type an integer or a simplified fraction.)
Answer
Final Answer: The probability of rolling a sum not more than 9 is \(\boxed{\frac{5}{6}}\).
Step 1 ：There are total 36 possible outcomes when a pair of dice is rolled.
Step 2 ：We need to find the number of outcomes where the sum of numbers on the dice is not more than 9. The favorable outcomes are 30.
Step 3 ：The probability is calculated as the ratio of favorable outcomes to total outcomes, which is approximately 0.8333.
Step 4 ：However, we need to simplify this fraction to its lowest terms. The simplified probability is \(\frac{5}{6}\).
Step 5 ：Final Answer: The probability of rolling a sum not more than 9 is \(\boxed{\frac{5}{6}}\).
