Probability
Two Biased Dice Probability
nta_pyq_2025_apr
Grade 12

Question:

One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5, when both the dice are thrown together, is
$\frac{2}{3}$
$\frac{1}{2}$
$\frac{4}{9}$
$\frac{3}{5}$

Step-by-Step Solution

Key Concept: List all ordered pairs (face of die 1, face of die 2) that sum to 4 or 5, multiplying their respective face probabilities.
Pairs summing to 4 or 5: (1,3),(1,4),(2,2),(2,3),(3,1),(3,2),(4,1). P $= \frac{2}{6}\cdot\frac{2}{6}+\frac{2}{6}\cdot\frac{1}{6}+\frac{2}{6}\cdot\frac{2}{6}+\frac{2}{6}\cdot\frac{2}{6}+\frac{1}{6}\cdot\frac{1}{6}+\frac{1}{6}\cdot\frac{2}{6}+\frac{1}{6}\cdot\frac{1}{6} = \frac{18}{36} = \frac{1}{2}$.
Correct Answer: $\frac{1}{2}$

Master Probability with Mathbee

Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.

Start Practicing for Free