Question

# One card is randomly drawn from a deck of 52 playing cards. Find the probability that (i) the drawn card is red. (ii) the drawn card is an ace. (iii) the drawn card is red and a king. (iv) the drawn card is red or a king. [4 MARKS]

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Solution

## Each subpart: 1 Mark each In randomly drawing a card from 52 cards, the possible outcome is 52. i.e., n(S) = 52 (i) Let A denotes the event that the drawn card is red. Since the number of red cards is 26. So, n(A) = 26 ∴ P(A = a red card) =n(A)n(S)=2652=12 ii) Let B denotes the event that the drawn card is an ace. Since there are four aces in the deck So, n(B) = 4 ∴ P(B = an ace card) =n(B)n(S)=452=113 iii) Let C denotes the event that the drawn card is red and a king. Since there are only two cards which are red kings. So, n(C) = 2 ∴ P(C = card is red and a king) =n(C)n(S)=252=126 iv) Let D denotes the event that the drawn card is red or a king. We have 26 red cards, which include 2 kings and there are two more kings of black colour. So, n(D) = 26 + 2 = 28 ∴ P(D = card is red or a king) =n(D)n(S)=2852=713

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