Question

Two dice are thrown simultaneously What is the probability of getting two numbers whose product is even?

• A. $\frac{1}{2}$
• B. $\frac{3}{4}$
• C. $\frac{3}{8}$
• D. $\frac{5}{16}$

Answer 1

The correct option is B $\frac{3}{4}$

In a simultaneous throw of two dice we have n(S)=($6\times 6$)=36

Let E = event of getting two numbers whose product is even

Then $E=\left\{\right(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),$

$(4,4)(4,5),(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$

$\therefore n\left(E\right)=27$

$\therefore P\left(E\right)=\frac{n\left(E\right)}{n\left(S\right)}=\frac{27}{36}=\frac{3}{4}$