Question

A die is thrown once. Find the probability of getting: (i) A prime number. (ii) A number lying between 2 and 6.

Hint:

Always write the sample space first. Each outcome of a fair die is equally likely, so probability = \(\frac{\text{favourable outcomes}}{\text{total outcomes}}\).

Answer 1

Step 1: Write the sample space.
When a die is thrown, the sample space is \[ S = \{1, 2, 3, 4, 5, 6\} \] Total outcomes \( = 6 \).

Step 2: (i) Probability of getting a prime number.
Prime numbers between 1 and 6 are \( \{2, 3, 5\} \). \[ P(\text{prime}) = \frac{3}{6} = \frac{1}{2} \]
Step 3: (ii) Probability of getting a number lying between 2 and 6.
Numbers between 2 and 6 are \( \{3, 4, 5\} \). \[ P(\text{number between 2 and 6}) = \frac{3}{6} = \frac{1}{2} \]
Step 4: Conclusion.
(i) Probability of a prime number = \( \boxed{\frac{1}{2}} \)
(ii) Probability of a number between 2 and 6 = \( \boxed{\frac{1}{2}} \)