Question

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 $P(A\cup B)$

• A. $3/5$
• B. $0$
• C. $1$
• D. $2/5$

Answer 1

The correct option is C $1$

Simply speaking, any number on the dice is either less than $5$ or more than $3$ (since the range covers all the numbers from $1$ to $6$). Hence, required probability = $1$.
Alternate method:
$P(A\cup B)=P\left(A\right)+P\left(B\right)-P(A\cap B)=\frac{3}{6}+\frac{4}{6}-\frac{1}{6}=1$