Question 116375: a deck of cards has a total of 52 cards, consisting of 4 suits; (spades, hearts, diamonds, and clubs); and 13 cards in each suit.
a. find the probability that a card will be a queen
b. find the probability that a card will be a heart
c. find the probability that the card will be a queen or a heart.
d. find the probability that a card will be the queen of hearts.
Found 2 solutions by solver91311, Fombitz:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Finding the answer to all four parts of this question is the exact same process, so I'm going to do one of them and let you do the rest.
All probability calculations involve finding two numbers: One is the number of possible outcomes of an event, and the second is the number of those outcomes that you consider successes. Then you divide the second number by the first to get your probability. Remember always that a probability is ALWAYS a number in the interval:  . Zero and 1 are included because sometimes the probability is that there is no possibility, such as the probability of drawing a Joker from a deck of 52 cards that doesn't have a Joker in it. That would obviously be p = 0 because there are 0 successful outcomes in the numerator of the fraction. On the other hand, some probabilities are certainties, such as the probability of drawing a heart from a pack of 13 cards consisting only of hearts.
In this problem you have a deck of 52 cards, so drawing one card means that there are exactly 52 different outcomes. Part c. of your problem asks what is the "probability that the card will be a queen or a heart"? So the problem becomes counting the number of the total 52 outcomes that would be considered a success, namely how many hearts and queens are there? You are given that there are 13 cards in each suit, and that there are 4 suits. Since there are 4 suits, that means there must be 4 queens. So, with 13 hearts and 4 queens, we have 17 possibilities, right? Wait a minute! One of those 13 hearts is the Queen of Hearts, so if we just add 13 plus 4, we have counted that card twice, so the correct number of successes is obtained by adding the number of hearts that aren't the Queen (12) to the number of Queens (4) obtaining 16.
Now your probability that the card is either a heart or a Queen is  , roughly 31%
You should be able to do the other three parts using the method for solving part c. But if you still have trouble, write back.
Super-Double-Plus Extra Credit:
What is the probability that you will get either a head or a tail when you flip a coin? (Hint: This is a trick question. Consider ALL the possibilities)
Hope this helps,
John
Answer by Fombitz(32388)  (Show Source):
You can put this solution on YOUR website! A) There are 4 queens in 52 cards.
P(Queen) = 4/52 = 1/13
B) There are 13 hearts in 52 cards.
P(Heart) = 13/52 = 1/4
C) From above, P(Queen)=4/52 and P(Heart)=13/52, the queen of hearts is in both categories so we have to subtract 1/52 so we don't double count.
P(Queen or Heart) = 4/52 + 13/52 - 1/52=16/52=4/13
D) There is only 1 queen of hearts in 52 cards.
P(Queen of Hearts) = 1/52
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