Question

Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is

• A.
  $\frac{1}{9}$
• B.
  $\frac{2}{9}$
• C.
  $\frac{1}{3}$
• D.
  $\frac{4}{9}$

Answer 1

The correct option is B

$\frac{2}{9}$
Sample space = 6 x 6 = 36 events = Total chances

Product of numbers on 2 dice have to perfect square = Favourable chances

(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6) (1, 4) (4, 1) $\Rightarrow$ 8 events

$Probability=\frac{Favourablechances}{Totalchances}=\frac{8}{36}=\frac{2}{9}$