What is the chance of throwing a sum greater than or equal to 7 in a throw of…

2025

What is the chance of throwing a sum greater than or equal to 7 in a throw of 2 dice?

  1. A.

    7/12

  2. B.

    1/3

  3. C.

    1/4

  4. D.

    2/5

Attempted by 1 students.

Show answer & explanation

Correct answer: A

Concept: When two fair dice are thrown, each die can show one of 6 faces, so there are 6 x 6 = 36 equally likely ordered outcomes. The probability of an event is (number of favourable outcomes) divided by (total number of outcomes).

Application: List how many ordered pairs give each possible sum from 7 through 12, then add them up:

Sum

Number of ordered pairs

7

6

8

5

9

4

10

3

11

2

12

1

  1. Add the favourable outcomes for every sum from 7 to 12: 6 + 5 + 4 + 3 + 2 + 1 = 21.

  2. Divide by the total number of outcomes: 21/36.

  3. Simplify 21/36 by dividing the numerator and denominator by 3: 21/36 = 7/12.

Cross-check: The complementary event is a sum of 6 or less. Counting those ordered pairs gives 1 (sum 2) + 2 (sum 3) + 3 (sum 4) + 4 (sum 5) + 5 (sum 6) = 15 outcomes. Since 36 - 15 = 21, this matches the favourable count found above.

So the required probability of throwing a sum of 7 or more with two dice is 7/12.

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