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]

(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

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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