Question

Two different dice are rolled together. The probability that both the obtained numbers are less than 4, is

• A. \(\frac{2}{9}\)
• B. \(\frac{7}{36}\)
• C. \(\frac{1}{4}\)
• D. \(\frac{2}{3}\)

Hint:

If events are independent (like rolling two dice), you can multiply individual probabilities: \(P(A \cap B) = P(A) \times P(B)\). Here, \(P(\text{die }<4) = 3/6 = 1/2\). So, \((1/2) \times (1/2) = 1/4\).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Probability is defined as the number of favorable outcomes divided by the total number of outcomes.
Step 2: Key Formula or Approach:
Total outcomes for two dice = \(6 \times 6 = 36\).
Numbers less than 4 on a single die are \(\{1, 2, 3\}\).
Step 3: Detailed Explanation:
For both numbers to be less than 4, the outcomes are:
\((1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)\).
Number of favorable outcomes = \(3 \times 3 = 9\).
\[ P(\text{both }<4) = \frac{9}{36} = \frac{1}{4} \]
Step 4: Final Answer:
The probability is \(\frac{1}{4}\).