A card is drawn at random from a well shuffled pack of 52 cards. Find the probability of drawing (i) a club, (ii) a king or an ace, (iii) not a spade
Answers
There are 52 cards in a deck of cards. One card is drawn at random.
∴ The number of all possible outcomes in the experiment of drawing a card = 52
(i) Let A be the event 'the card drawn is a club'.
There are 13 club cards in a deck.
∴ The number of outcomes favourable to A is 13.
∴ P(A) = 13/52 = 1/4
(ii) Let B be the event 'the card drawn is a king or an ace'.
There are 4 kings cards and 4 ace cards in a deck.
∴ The number of outcomes favourable to B is 8 (4+4).
∴ P(B) = 8/52 = 2/13
(iii) Let C be the event 'the card drawn is a spade'.
There are 13 spade cards in a deck.
∴ The number of outcomes favourable to C is 13.
∴ P(C) = 13/52 = 1/4
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EXPLANATION.
A card is drawn at random for a well shuffled pack of 52 cards.
As we know that,
Probability = Number of favorable outcomes/Total number of outcomes.
Total number of outcomes = 52.
(1) a club.
A club contains 13 cards.
1 king, 1 queen, 1 jack, 1 ace, 2- 10 cards.
Number of favorable outcomes = 13.
Probability = 13/52. = 1/4.
Probability = 1/4.
(2) a king Or an ace
A king contains 4 cards.
A ace also contains 4 cards.
Number of favorable outcomes = 4 + 4 = 8.
Probability = 8/52. = 2/13.
Probability = 2/13.
(3) Not a spade.
Number of spade card = 13.
Total number of cards = 52.
Not a spade card = 52 - 13 = 39.
Number of favorable outcomes = 39.
Probability = 39/52.
Probability = 3/4.