Question

The probability of getting a sum greater than 7 when a pair of dice are thrown is:

• A. \( \frac{7}{36} \)
• B. \( \frac{5}{12} \)
• C. \( \frac{7}{12} \)
• D. \({None of these}\)

Hint:

When solving probability problems involving dice, listing favorable outcomes systematically helps avoid errors.

Answer 1

The Correct Option is B

Step 1: Total Outcomes When Rolling Two Dice When two fair dice are rolled, each die has 6 faces, leading to a total number of possible outcomes: \[ 6 \times 6 = 36. \] 
Step 2: Favorable Outcomes Where Sum \(>7 \) We list all possible pairs \( (x,y) \) where the sum \( x+y \) is greater than 7 
- Sum = 8: \( (2,6), (3,5), (4,4), (5,3), (6,2) \) (5 outcomes) 
- Sum = 9: \( (3,6), (4,5), (5,4), (6,3) \) (4 outcomes) - Sum = 10: \( (4,6), (5,5), (6,4) \) (3 outcomes) 
- Sum = 11: \( (5,6), (6,5) \) (2 outcomes) 
- Sum = 12: \( (6,6) \) (1 outcome) Total favorable outcomes: \[ 5 + 4 + 3 + 2 + 1 = 15. \] 
Step 3: Probability Calculation The probability of getting a sum greater than 7 is: 
\[ \frac{{Favorable outcomes}}{{Total outcomes}} = \frac{15}{36} = \frac{5}{12}. \]