Question

5 cards are drawn from a standard deck without replacement. What is the probability that at least one of the cards drawn is a spade? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

A "standard" deck of playing cards consists of 52 Cards in each of the 4 suits of Spades, Hearts, Diamonds, and Clubs. Each suit contains 13 cards: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King.

hence

the total number of cards  

we want the probability that at least one of the cards drawn is a spade.

we can use the following formula

in a spade suit, there are 13 cards.

let S be the event that none of the cards is spade then

5 cards are drawn from a standard deck without replacement then the probability of no spade is given by

hence