Question

Two dice are rolled simultaneously. Find the probability that number appearing on the first die is of the form of 5p or 2p and the number appearing on the second die is of the form 3q. (where 'p' and‘q’ can take values 1, 2 or 3).

• A.
  $\frac{5}{36}$
• B.
  $\frac{1}{6}$
• C.
  $\frac{2}{9}$
• D.
  $\frac{7}{36}$

Answer 1

The correct option is C

$\frac{2}{9}$

Total no. of outcomes= 36
Number appearing on the first die is of the form of 5q, means it must be a multiple of 5 and if of the form of 2q then it must be multiple of 2.
Number appearing on the second die is of the form of 3q, means it must be a multiple of 3.
For an event $\text{E, Probability P(E)}$ = $\frac{\text{Number of outcomes favourable to E}}{\text{Number of all possible outcomes of the experiment}}$
Favourable outcomes = {(5, 3), (5, 6), (2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6)}.

Required probability $=\frac{8}{36}=\frac{2}{9}$