Question

The faces of a dice are marked with numbers 1, 1, 2, 4, 5, 5 and that of another dice with number 2, 3, 4, 5, 6, 6. Both dice are thrown together once. What is the probability that the sum of numbers on their tops is odd?

• A.
  $\frac{2}{9}$
• B.
  $\frac{5}{18}$
• C.
  $\frac{4}{9}$
• D.
  $\frac{5}{9}$

Answer 1

The correct option is D

$\frac{5}{9}$
Numbers on faces of first die are 1, 1, 2, 4, 5, 5 (six outcomes).

Numbers on faces of second die are 2, 3, 4, 5, 6, 6 (six outcomes).

$\therefore$ Total number of outcomes $=6\times 6=36$

Outcomes having sum of numbers on their tops as odd are (1, 2), (1, 2), (1, 4), (1, 4), (1, 6), (1, 6), (1, 6), (1, 6), (2, 3), (2, 5), (4, 3), (4, 5), (5, 2), (5, 2), (5, 4), (5, 4), (5, 6), (5, 6), (5, 6), (5, 6)

Number of favourable outcomes = 20

$\therefore$ Required probability $=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\frac{20}{36}=\frac{5}{9}$


Hence, the correct answer is option (d).