Question

Two dice are thrown simultaneously. The probability of getting the sum as prime is

• A.
  $\frac{1}{6}$
• B.
  $\frac{3}{17}$
• C.
  $\frac{5}{12}$
• D.
  $\frac{1}{4}$

Answer 1

The correct option is C

$\frac{5}{12}$
Total number of outcomes obtained on throwing two dice
$=6\times 6=36$

Outcomes for getting the sum as prime are $(1,1),(1,2),(1,4),(1,6),(2,1),(2,3),(2,5),(3,2),(3,4),(4,1),(4,3),(5,2),(5,6),(6,1),(6,5).$

$\therefore$ Number of favourable outcomes = 15

$\therefore$ Required probability

$=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{15}{36}=\frac{5}{12}$

Hence, the correct answer is option (c).