Question

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

• A. $\frac{1}{4}$
• B. $\frac{3}{4}$
• C. $\frac{5}{12}$
• D. $\frac{7}{12}$

Answer 1

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

Product of two numbers is even if either one or both of them are even.

Thus, an odd number can multiply with $3$ even numbers to become even, & an even number can multiply with all numbers.

$\therefore$ pairs are;

$(1,2)$ $(2,1)$ $(3,2)$ ................. $(6,1)$

$(1,4)$ $(2,2)$ $(3,4)$ $.$ .

$(1,6)$ $.$ $.$ $.$

$.$ $.$ $.$

$.$ $.$ $.$

$(2,6)$ $(3,6)$ $(6,6)$

$\_\_\_\_\_\_3pair\_\_\_\_\_\_$ $\_\_\_\_\_\_6pair\_\_\_\_\_\_$ $\_\_\_\_\_\_3pair\_\_\_\_\_\_$ $\_\_\_\_\_\_6pair\_\_\_\_\_\_$

which total to $27$ pairs which can form even numbers

$\therefore P[Product=even]=\frac{27}{6^2}=\frac{27}{36}=\frac{3}{4}$