Q. 54.5( 2 Votes )

From a deck of cards, three cards are drawn on by one without replacement. Find the probability that each time it is a card of spade.

Answer :

Total number of all favorable cases is n(S) = 52


Let A be the event that first card drawn is card of spade. There are 13 spade cards in the pack. Hence, the probability of the first card is spade is



Let B be the event that second card is also card of spade without replacement. Then there are 12 spade cards left in the pack as the cards are not replaced. Therefore, the probability of the second card is also spade card is



Let C be the event that third card is also spade card without replacement. Then there are 11 spade cards left in the pack as the cards are not replaced. Therefore, the probability of the third card is also a spade card is



Then the probability all three are spade cards without replacement is



(as there are 13 spade cards in the pack of 52 in first draw, 12 spade cards in the pack of 51cards in the second draw as the cards are not replaced and 11spadecards in the pack of 50 cards in the third draw as the cards are not replaced.)


The required probability is


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