Question

Two biased dice are rolled. Out of which one die contains 1, 1, 2, 2, 3, 3, and another die contains 1, 2, 2, 3, 3, 4. Then the probability of getting a sum of 4 or 5 is:

• A. \( \frac{7}{36} \)
• B. \( \frac{1}{9} \)
• C. \( \frac{5}{36} \)
• D. \( \frac{1}{6} \)

Hint:

When calculating probability, first list all the successful outcomes and divide by the total number of possible outcomes.

Answer 1

The Correct Option is C

We need to calculate the probability of getting a sum of 4 or 5 when two dice are rolled. First, list all possible outcomes that result in a sum of 4 or 5: - For a sum of 4: Possible outcomes are (1, 3), (2, 2), (3, 1) — 3 outcomes. - For a sum of 5: Possible outcomes are (1, 4), (2, 3), (3, 2), (4, 1) — 4 outcomes. Total successful outcomes = 3 (for 4) + 4 (for 5) = 7 outcomes. The total number of possible outcomes when two dice are rolled is \( 6 \times 6 = 36 \). Thus, the probability is \( \frac{7}{36} \). Thus, the correct answer is \( \frac{7}{36} \).