A black and a red die are rolled together. Find the conditional probability of obtaining the sum 6, given that the red die resulted in a number less than 3.

1/6

The correct answer is Option 4: 1/6

Step 1: Define the condition

• Red die shows a number less than 3 → possible outcomes: {1, 2}.
  So there are 2 choices for red die.

• Black die can take values {1,2,3,4,5,6} → 6 choices.

Thus, total favorable cases under the condition = 2 × 6 = 12.

Step 2: Find favorable cases (sum = 6)

We need black die + red die = 6.

• If red = 1 → black must be 5 (valid).

• If red = 2 → black must be 4 (valid).

So there are 2 favorable outcomes.

Step 3: Compute conditional probability

P(sum=6 | red < 3)= favorable outcomes/ total outcomes under condition 

                                = 2 / 12

                                = 1/6