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:

Since rolling two separate dice are independent events, you can find the individual probabilities and multiply them:
- Probability of getting a number less than 4 on the first die is \(\frac{3}{6} = \frac{1}{2}\).
- Probability of getting a number less than 4 on the second die is \(\frac{3}{6} = \frac{1}{2}\).
- Since they are independent, the total probability is:
\[ P = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \] This product rule is extremely fast and prevents you from having to list out all the coordinate pairs!

Answer 1

The Correct Option is C

Step 1: Treat the two dice as independent events.
Rolling the first die and the second die are independent, so we can multiply their individual probabilities.
Step 2: Find the probability for a single die.
Numbers less than 4 on one die are $1, 2, 3$, so $P(\text{one die} \lt 4) = \frac{3}{6} = \frac{1}{2}$.
Step 3: Multiply the two probabilities.
\[ P(\text{both} \lt 4) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \]
\[ \boxed{\frac{1}{4}} \]