Question

The Probability of getting a number greater than 2 with a throw of fair dice is :

• A. \(\frac{2}{3}\)
• B. \(\frac{5}{6}\)
• C. \(\frac{1}{3}\)
• D. \(\frac{3}{4}\)

Hint:

1. A fair die has outcomes: {1, 2, 3, 4, 5, 6}. Total outcomes = 6. 2. "Number greater than 2" means the outcomes: {3, 4, 5, 6}. Favorable outcomes = 4. 3. Probability = (Favorable outcomes) / (Total outcomes) = \(\frac{4}{6}\). 4. Simplify the fraction: \(\frac{4}{6} = \frac{2}{3}\).

Answer 1

The Correct Option is A

Concept: Probability of an event = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\). A fair die has 6 faces, numbered 1, 2, 3, 4, 5, 6. Step 1: Identify the total number of possible outcomes When a fair die is thrown, the possible outcomes are \{1, 2, 3, 4, 5, 6\}. Total number of possible outcomes = 6. Step 2: Identify the favorable outcomes We want the probability of getting a number "greater than 2". The numbers on the die that are greater than 2 are \{3, 4, 5, 6\}. Number of favorable outcomes = 4. Step 3: Calculate the probability Probability (number>2) = \(\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\) \[ P(\text{number}>2) = \frac{4}{6} \] Step 4: Simplify the fraction The fraction \(\frac{4}{6}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. \[ \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \] The probability of getting a number greater than 2 is \(\frac{2}{3}\). This matches option (1).