Correct Answer - Option 2 : 1/9
Given:
A dice is rolled twice.
Formula used:
Probability of an event E, P(E), is defined as
P(E) = (Number of outcomes favourable to E)/(Number of all possible outcomes of the experiment)
= n(E) / n(S)
Calculation:
The sample space S when a dice is rolled twice is,
S = { (1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6) }
Four possible outcomes give a sum equal to 5 are {(1, 4), (2, 3), (3, 2), (4, 1)}
And, Total possible outcomes = 36
∴ P(E) = n(E) / n(S) = 4 / 36 = 1 / 9
