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  • 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 c

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.

Answers (1)

(a) We know that, the possible outcomes of a fair die are-

S = {1, 2, 3, 4, 5, 6}

Thus, total no. of outcomes = 6

Here, 1, 3 & 5 are odd nos.

Thus, favorable outcomes = 3

Probability = no. of favorable outcomes/ total no. of outcomes

                        = 3 / 6

                        = 1/2

(b) When a fair coin is tossed twice,

S = {HH, HT, TH, TT}

Thus, total n, of outcomes = 4

For at least one head to appear, the possible cases will be – HH, HT, TH

Thus, favorable outcomes = 3

Now, 

Probability = no. of favorable outcomes/ total no. of outcomes

                  = 3/ 4

  1. When we roll a pair of dice,

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)}

Thus, n(S) = 36

For sum to be 6, the possible outcomes will be –

(1,5), (2,4), (3,3), (4,2), (5,1)

Thus, favorable outcomes = 5

Probability = no. of favorable outcomes/ total no. of outcomes

                  = 5/ 36

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