Question

A man is dealt 4 spade cards from an ordinary pack of 52 cards. if he is given three more cards, find the probability p that at least one of the additional cards is also a spade.

Answer 1

9/52 is the probability

Answer 2

Given an ordinary deck of card and a man dealt four spade cards , find probability one of the additional three cards dealt is also a spade

Explanation:  

1. probability of choosing a particular card from a deck of cards is given by,             $P(p)=\frac{no.\ of\ desired\ cards}{total\ no.\ of\ cards}$  
2. since, four cards ( $4$ spades out of total $13$) are already dealt the total number cards are now $48$  and number of spades available are $9$.
3. hence, the probability of getting at least one spade on additional three cards is given as, $p= 1-P(no\ card\ dealt\ is\ spade)$    
4. now, the number of cards that are not spade are $48-9=39$                                    $P(p)=1-\frac{C_3^{39}}{C_3^{48}} =1-\frac{9,139}{17,296} \\P(p)= \frac{8,157}{17,296} = 0.47$  
5. hence, the probability that at least one of the additional card is a spade is $0.47$.