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?
- A.
7/12
- B.
1/3
- C.
1/4
- 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 |
Add the favourable outcomes for every sum from 7 to 12: 6 + 5 + 4 + 3 + 2 + 1 = 21.
Divide by the total number of outcomes: 21/36.
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.
