Question

When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other die is:

• A. \( \frac{1}{6} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{1}{2} \)
• D. \( \frac{1}{4} \)

Hint:

For two-dice probability questions: - First find all possible outcomes (usually 36). - Count favorable outcomes carefully. - If order can change (Prime-Composite and Composite-Prime), include both cases.

Answer 1

The Correct Option is B

Concept: Probability is given by: \[ P(E)=\frac{{Favorable Outcomes}}{{Total Outcomes}} \] For two dice: \[ {Total outcomes}=6 \times 6=36 \] Prime numbers on a die are: \[ 2,3,5 \] So number of prime outcomes: \[ 3 \] Composite numbers on a die are: \[ 4,6 \] So number of composite outcomes: \[ 2 \] Since either die can show prime or composite, both arrangements must be considered.
Step 1: Find total number of outcomes when two dice are thrown. \[ 6 \times 6=36 \] Thus, \[ {Total outcomes}=36 \]
Step 2: Find favorable outcomes for one prime and one composite. Case 1: First die shows prime and second die shows composite \[ 3 \times 2=6 \] Case 2: First die shows composite and second die shows prime \[ 2 \times 3=6 \] Total favorable outcomes: \[ 6+6=12 \]
Step 3: Calculate the required probability. \[ P=\frac{12}{36} \] \[ =\frac{1}{3} \]