A die is thrown Find the probability of getting an odd number

HSC 12th Board Exam: Mathematics Probability Solution

Question

A die is thrown. Find the probability of getting an odd number.

Detailed Solution

Step 1: Determine the Sample Space (S)

When a standard six-sided die is thrown, the possible outcomes are numbers from 1 to 6.
\[ S = \{1, 2, 3, 4, 5, 6\} \] Therefore, the total number of possible outcomes is: \[ n(S) = 6 \]

Step 2: Define Event A

Let \( A \) be the event of getting an odd number.
The odd numbers on a die are 1, 3, and 5.
\[ A = \{1, 3, 5\} \] Therefore, the number of favorable outcomes is: \[ n(A) = 3 \]

Step 3: Calculate Probability

The probability of an event is given by the formula: \[ P(A) = \frac{n(A)}{n(S)} \]

Substituting the values: \[ P(A) = \frac{3}{6} \]

Simplifying the fraction: \[ P(A) = \frac{1}{2} \]

Answer: The probability of getting an odd number is \( \frac{1}{2} \).