Question

Two dice are thrown simultaneously. The probability of getting a multiple of 2 on one die and a prime number on the other die is

• A.
  $\frac{1}{3}$
• B.
  $\frac{5}{18}$
• C.
  $\frac{17}{36}$
• D.
  $\frac{7}{36}$

Answer 1

The correct option is C

$\frac{17}{36}$
When two dice are thrown simultaneously, the total number of possible outcomes is $6^2=36.$

Favourable outcomes of getting multiple of 2 on one die and a prime number on other die are $(2,2),(2,3),(2,5),(4,2),(4,3),(4,5),(6,2),(6,3),(6,5)(3,2),(5,2),(2,4),(3,4),(5,4),(2,6),(3,6),(5,6).$

$\therefore$Number of favourable outcomes = 17

$\therefore$ Required probability

$=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{17}{36}$
Hence, the correct answer is option c.