Question

q 24.) the table below shows the sums of two number cubes being rolled. what is the probability that the sum will be less than 8? express your answer to the nearest whole percent.

Explanation:

Step1: Count total outcomes

The total number of outcomes when rolling two number - cubes is \(6\times6 = 36\) since each cube has 6 faces.

Step2: Count favorable outcomes

The sums less than 8 are 2, 3, 4, 5, 6, 7.
For sum = 2: (1,1) - 1 way
For sum = 3: (1,2), (2,1) - 2 ways
For sum = 4: (1,3), (2,2), (3,1) - 3 ways
For sum = 5: (1,4), (2,3), (3,2), (4,1) - 4 ways
For sum = 6: (1,5), (2,4), (3,3), (4,2), (5,1) - 5 ways
For sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) - 6 ways
The total number of favorable outcomes is \(1 + 2+3 + 4+5 + 6=21\).

Step3: Calculate probability

The probability \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{21}{36}=\frac{7}{12}\).

Step4: Convert to percentage

\(P=\frac{7}{12}\times100\% \approx 58.33\%\approx58\%\) (rounded to the nearest whole percent)

Answer:

58%