Question

Probability of getting a number \(>4\) on a fair die is:

• A. \( \frac{1}{2} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{1}{6} \)
• D. \( \frac{2}{3} \) Correct Answer: (B) \( \frac{1}{3} \) Solution:

Hint:

For a fair die: \[ P(E)=\frac{\text{Favourable Outcomes}}{6} \] Always count the outcomes carefully before applying the probability formula.

Answer 1

The Correct Option is B

Concept: Probability measures the likelihood of occurrence of an event. For equally likely outcomes, \[ P(E) = \frac{\text{Number of favourable outcomes}} {\text{Total number of outcomes}} \] where \(P(E)\) denotes the probability of event \(E\).

Step 1: List the outcomes of a fair die. A fair die has six possible outcomes: \[ \{1,2,3,4,5,6\} \] Therefore, \[ \text{Total outcomes}=6 \]

Step 2: Determine the favourable outcomes. The event is obtaining a number greater than 4. The favourable outcomes are: \[ \{5,6\} \] Thus, \[ \text{Number of favourable outcomes}=2 \]

Step 3: Apply the probability formula. \[ P(\text{number}>4) = \frac{2}{6} \] \[ = \frac{1}{3} \]

Step 4: State the final answer. Hence, \[ \boxed{\frac{1}{3}} \] is the required probability. Therefore, the correct option is \(\boxed{(B)}\).