Question

Two dice each numbered from $1$ to $6$ are thrown together. Let $A$ and $B$ be two events given by

$A:$ even number on the first die

$B:$ number on the second die is greater than $4$

Find the value of $P(A\cap B).$

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{2}{3}$
• D. $\frac{1}{6}$

Answer 1

The correct option is D $\frac{1}{6}$

Given:

Two dice are thrown, hence the total number of all possible ways, $n\left(S\right)=$ $6\times 6=36$

A: even number on the first die

B: the number on the second die is greater than $4$

To find:

$P(A\cap B)$

And, $A\cap B$, means even number on first die and number greater than $4$ on second die i.e., $\left\{\right(2,5),(2,6),(4,5),(4,6),(6,5),(6,6\left)\right\}=6$

Hence, $P(\cap B)=\frac{6}{36}=\frac{1}{6}$