Considering an experiment of tossing two fair dice, one black and one red.…
2015
Considering an experiment of tossing two fair dice, one black and one red. What is the probability that the number on the black die divides the number on red die ?
- A.
\(\dfrac{22}{36} \\\) - B.
\(\dfrac{12}{36} \\\) - C.
\(\dfrac{14}{36} \\\) - D.
\(\dfrac{6}{36}\)
Attempted by 57 students.
Show answer & explanation
Correct answer: C
Approach: count ordered pairs (black, red) since the dice are distinguishable.
Total outcomes: 36 (6 faces on the black die × 6 faces on the red die).
Black = 1: 1 divides every red face → 6 favorable outcomes.
Black = 2: red = 2, 4, 6 → 3 favorable outcomes.
Black = 3: red = 3, 6 → 2 favorable outcomes.
Black = 4: red = 4 → 1 favorable outcome.
Black = 5: red = 5 → 1 favorable outcome.
Black = 6: red = 6 → 1 favorable outcome.
Favorable outcomes: 6 + 3 + 2 + 1 + 1 + 1 = 14
Probability = 14/36 = 7/18.
Final answer: 14/36 (which simplifies to 7/18).