Q.33 Two fair six-sided dice are thrown. The probability of getting 12 as the product of the numbers on the dice (rounded off to two decimal places) is ____________.
Probability of Product 12 with Two Dice: 0.11
Two fair six-sided dice yield a product of 12 in exactly 4 outcomes out of 36 possible results. This gives a probability of 4/36 = 0.11 when rounded to two decimal places.
Total Outcomes
Each die shows numbers 1 through 6, creating 6×6 = 36 equally likely outcomes. All combinations like (1,1) through (6,6) form the sample space.
Favorable Outcomes
The pairs where the product equals 12 are:
- (2,6):
2×6 = 12 - (3,4):
3×4 = 12 - (4,3):
4×3 = 12 - (6,2):
6×2 = 12
No other pairs work, as factors like 1×12 or 12×1 exceed die faces.
Probability Calculation
Probability = 4/36 = 1/9 ≈ 0.1111. Rounded to two decimal places: 0.11.
Introduction: Unlocking Probability of Product 12 with Two Dice
In probability problems involving two fair six-sided dice, finding the probability of getting 12 as the product of the numbers requires listing factor pairs within 1-6. This classic question tests sample space and favorable outcomes, yielding 0.11 when rounded to two decimal places—ideal for competitive exams.
Step-by-Step Solution for Product 12 Dice Probability
- Sample Space: 36 total outcomes from 6×6 rolls.
- Factor Pairs for 12: Only (2,6), (3,4), (4,3), (6,2) qualify.
- Probability Formula:
P = 4/36 = 0.1111 ≈ 0.11.
No other options exist—pairs like (1,12) are invalid.
Common Mistakes to Avoid
- Forgetting order matters: (3,4) ≠ (4,3)
- Including invalid faces beyond 6
- Misrounding: 0.1111 becomes 0.11, not 0.1 or 0.12
Why This Matters for Exams
This mirrors IIT JAM-style questions on discrete probability, building skills in counting principles.
Keywords
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