Question

In a simultaneous throw of a pair of dice, find the probability of getting 2 will not come either time.

Answer 1

Total Outcomes: When a pair of dice is thrown simultaneously, the sample space consists of:

\[ S = {(1,1), (1,2), \dots, (6,6)} \] 

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

2 will not come either time:

Outcomes where 2 appears at least once: ({(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (1, 2), (3, 2), (4, 2), (5, 2), (6, 2)}) (11 outcomes).

Outcomes where 2 does not appear either time: (36 – 11 = 25) 

\[P(\text{2 will not come either time}) = \dfrac{25}{36}\]