SOLUTION: If six cards are drawn from a deck of cards without replacement, what is the probability that at least one of the cards is a spade?

Algebra.Com
Question 1147394: If six cards are drawn from a deck of cards without replacement, what is the probability that at least one of the cards is a spade?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
This is 1- probability none of the cards is a spade
That is 1-(0.75^6)=0.8220
Answer by ikleyn(52797)   (Show Source): You can put this solution on YOUR website!
.
This is  1 - probability that NO ONE af the six cards is a spade.



The probability that the 1-st card in not a spade is  .

The probability that the 2-nd card in not a spade is  .

The probability that the 3-rd card in not a spade is  .

The probability that the 4-th card in not a spade is  .

The probability that the 5-th card in not a spade is  .

The probability that the 6-th card in not a spade is  .


Therefore, the probability under the question is


    P =  = 0.8397.    ANSWER


RELATED QUESTIONS

If five cards are drawn from a deck of cards without replacement what is the probability... (answered by lynnlo)
6 cards are drawn from a standard deck without replacement. What is the probability that (answered by stanbon)
Five cards are drawn from a standard deck without replacement. What is the probability... (answered by greenestamps)
In a standard deck of 52 playing cards, two cards are known: the 2 of hearts, and the 2... (answered by greenestamps)
From a standard deck of cards, first two cards are drawn from the deck without... (answered by ewatrrr)
4 cards are drawn from a standard deck without replacement. What is the probability that (answered by greenestamps)
5 cards are drawn from a standard deck without replacement. What is the probability that (answered by Boreal)
I need help on this one please. 9. If 2 cards are drawn (without replacement) from a... (answered by rothauserc)
A deck of playing cards contains 26 red and 26 black cards. Two cards are drawn from the... (answered by Nate)