A die is thrown. Let $A$ be the event that the number obtained is greater than 3. Let $B$ be the event that the number obtained is less than 5. Then $P(A\cup B)$ is

$S = \{1, 2, 3, 4, 5, 6\}$ $A: \text{number} > 3, \qquad B: \text{number} < 5$ $\text{To find: } P(A \cup B)$ $1.\ \text{write } S, A, B$ $2.\ \text{find } A \cap B \text{ and } A \cup B$ $3.\ P(A \cup B) = P(A) + P(B) - P(A \cap B)$ $S = \{1,2,3,4,5,6\}$ $A = \{4,5,6\}, \quad B = \{1,2,3,4\}$ $A \cap B = \{4\}$ $A \cup B = \{1,2,3,4,5,6\} = S$ $P(A) = \dfrac{3}{6}, \quad P(B) = \dfrac{4}{6}, \quad P(A \cap B) = \dfrac{1}{6}$ $P(A \cup B) = P(A) + P(B) - P(A \cap B) = \dfrac{3+4-1}{6} = \dfrac{6}{6} = 1$ $\boxed{P(A \cup B) = 1 \ \Rightarrow \ \text{option } (3)}$