Determine the probability p, for each of the following events.

(a) An odd number appears in a single toss of a fair die.

(b) At least one head appears in two tosses of a fair coin.

(c) A king, 9 of hearts, or 3 of spades appears in drawing a single card from a well shuffled ordinary deck of 52 cards.

(d) The sum of 6 appears in a single toss of a pair of fair dice.

(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,