If 3 dice are rolled and a, b, c is obtained what is the probability that…
2023
If 3 dice are rolled and a, b, c is obtained what is the probability that a*b+c is even ?
- A.
7/2
- B.
5/2
- C.
1/2
- D.
3/2
Attempted by 36 students.
Show answer & explanation
Correct answer: C
Answer: 1/2
Total possible outcomes when three dice are rolled: 6 × 6 × 6 = 216.
We need a*b + c to be even, so parity(a*b) must equal parity(c). Count favorable outcomes in two cases:
Case 1 — a*b is odd: This occurs only when both a and b are odd. Number of odd faces = 3, so (a,b) odd pairs = 3 × 3 = 9. For a*b odd we need c odd (3 choices). Favorable outcomes = 9 × 3 = 27.
Case 2 — a*b is even: This happens when at least one of a or b is even. Total (a,b) pairs = 36, so even-product pairs = 36 − 9 = 27. For a*b even we need c even (3 choices). Favorable outcomes = 27 × 3 = 81.
Total favorable outcomes = 27 + 81 = 108.
Probability = 108 / 216 = 1/2.