Question

A pair of dice is rolled, and the number that appears uppermost on each die is observed. Refer to this experiment, and find the probability of the given event. (Enter your answer as a fraction.)
The sum of the numbers is at least 4.

Answer 1

Answer:

• 11/12 ≈ 0.92

Explanation:

You can find the theoretical probability of the event "the sum of the numbers is at least 4".

The theoretical probability is:

• number of positive outcomes / number of possible outcomes.

1. Number of positive outcomes.

The number of positive outcomes is the amount of ways for which the sum of the numbers is at least 4.

Those are:

• Sum = 4: (1,3); (2,2), (3,1) → 3 ways

• Sum = 5: (1,4), (2,3), (3,2), (4,1) → 4 ways

• Sum = 6: (1,5), (2, 4), (3, 3), (4, 2), (5,1) → 5 ways

• Sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) → 6 ways

• Sum = 8: (2,6), (3,5), (4,4), (3,5), (2,6) → 5 ways

• Sum = 9: (3,6), (4,5), (5,4), (6,3) → 4 ways

• Sum = 10: (4,6), (5,5), (6,4) → 3 ways

• Sum = 11: (5, 6), (6,5) → 2 ways

• Sum = 12: (6,6) → 1 way

Thus, the total number of ways to have a sum of at least 4 is: 3 + 4 + 5 + 6 + 5 + 4 + 3 + 2 + 1 = 33.

2. Number of possible outcomes

The total number of possible outcomes is found by multiplying the ways each die can be rolled, this is: 6 × 6 = 36.

3. Probability

Then, the searched probability is 33/36 = 11/12 ≈ 0.92