Question

a pair of dice is rolled. find the probability of rolling
a) a sum not more than 6,
b) a sum not less than 4,
c) a sum between 3 and 8 (exclusive).

Explanation:

Step1: Find total number of outcomes

When rolling two dice, each die has 6 possible outcomes. So the total number of outcomes when rolling two dice is $6\times6 = 36$.

Step2: Find number of favorable outcomes for sum not more than 6

The possible sums and their combinations are:

• Sum = 2: (1,1) - 1 combination
• Sum = 3: (1,2), (2,1) - 2 combinations
• Sum = 4: (1,3), (2,2), (3,1) - 3 combinations
• Sum = 5: (1,4), (2,3), (3,2), (4,1) - 4 combinations
• Sum = 6: (1,5), (2,4), (3,3), (4,2), (5,1) - 5 combinations

The total number of favorable outcomes is $1 + 2+3 + 4+5=15$.

Step3: Calculate the probability

The probability $P$ is the number of favorable outcomes divided by the total number of outcomes. So $P=\frac{15}{36}=\frac{5}{12}$.

Answer:

$\frac{5}{12}$