(a) When a fair die is thrown, the possible outcomes are
S = {1, 2, 3, 4, 5, 6}
∴ total outcomes = 6
and the odd numbers are 1, 3, 5
∴ Favourable outcomes = 3
We know that,
(b) When a fair coin is tossed two times, the sample space is
S = {HH, HT, TH, TT}
∴ Total outcomes = 4
If at least one head appears then the favourable cases are HH, HT and TH.
∴ Favourable outcomes = 3
We know that,
(c) When a pair of dice is rolled, total number of cases
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)}
Total Sample Space, n(S) = 36
If sum is 6 then possible outcomes are (1,5), (2,4), (3,3), (4,2) and (5,1).
∴ Favourable outcomes = 5
We know that,
