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.
Answer & explanation
Correct answer: option 4
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