Question

Consider a random experiment of rolling a fair die. The probability of getting an odd number or a number less than 4 is ______ (Rounded off to two decimal places).

Hint:

List or count the die faces that are odd, less than 4, or both, and use the addition rule of probability to avoid double counting.

Answer 1

Correct Answer: 0.66

Step 1: Define the sample space and the two events.
For a fair die, the sample space is \(S = \{1, 2, 3, 4, 5, 6\}\), each outcome equally likely with probability \(1/6\). Let \(A\) = odd number \(= \{1, 3, 5\}\) and \(B\) = number less than 4 \(= \{1, 2, 3\}\).
Step 2: Apply the addition rule for probability.
\[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Here \(P(A) = 3/6\), \(P(B) = 3/6\), and \(A \cap B = \{1, 3\}\) so \(P(A \cap B) = 2/6\).
Step 3: Substitute and compute.
\[ P(A \cup B) = \frac{3}{6} + \frac{3}{6} - \frac{2}{6} = \frac{4}{6} = 0.6\overline{6} \approx 0.67 \] \[ \boxed{P(A \cup B) \approx 0.67} \]