Question

In a simultaneous throw of a pair of dice, find the probability of getting 5 at least once.

Answer 1

Total Outcomes: When a pair of dice is thrown simultaneously, the sample space consists of: \[ S = {(1,1), (1,2), \dots, (6,6)} \] 

\[ n(S) = 6 \times 6 = 36 \]

5 at least once: Favourable outcomes: ({(1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5), (5, 1), (5, 2), (5, 3), (5, 4), (5, 6)}) 

Number of favourable outcomes = 11

\[ P(5 \text{ at least once}) = \dfrac{11}{36} \]