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

To solve the problem of determining the probability that both numbers obtained by rolling two different dice are less than 4, we follow these steps:

1. Understand the total possible outcomes:
   • Each die has 6 faces, numbered from 1 to 6.
   • When two dice are rolled together, the total number of possible outcomes is \(6 \times 6 = 36\).
2. Identify favorable outcomes:
   • We need both dice to show numbers less than 4. Therefore, the numbers on each die can be 1, 2, or 3.
   • This gives us 3 choices for each die.
   • Hence, the number of favorable outcomes is \(3 \times 3 = 9\).
3. Calculate the probability:
   • The probability is the number of favorable outcomes divided by the total number of possible outcomes.
   • Thus, the probability \(P\) is given by: \(P = \frac{9}{36} = \frac{1}{4}\).
4. Conclusion:
   • The probability that both numbers obtained are less than 4 is \(\frac{1}{4}\). Therefore, the correct answer is \(\frac{1}{4}\).