Question

2 dice are thrown in the air. Find the probability of getting a sum less than 11.

• A. 7/12
• B. 11/12
• C. 5/12
• D. 1/3

Hint:

Always use the complement rule \( 1 - P(\text{Not } A) \) when asked for "less than" or "greater than" probabilities that contain many terms.
The total number of outcomes is 36.
The only sums that are NOT less than 11 are 11 (2 ways) and 12 (1 way).
This gives 3 outcomes out of 36.
Subtract from 1: \( 1 - \frac{3}{36} = 1 - \frac{1}{12} = \frac{11}{12} \).
This takes very little time to solve!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Total outcomes for 2 dice \( = 6 \times 6 = 36 \).
It's easier to find the probability of getting a sum \( \ge 11 \) and subtract from 1.
Step 2: Key Formula or Approach:
1. Total outcomes \( = 36 \).
2. Sums \( \ge 11 \): (5,6), (6,5) for sum 11, and (6,6) for sum 12.
Step 2: Detailed Explanation:
Total cases for sum \( \ge 11 = 3 \).
Probability of sum \( \ge 11 = 3/36 = 1/12 \).
Probability of sum \(<11 = 1 - 1/12 = 11/12 \).
Step 3: Final Answer:
The probability is 11/12.
Matches Option (B).