Question

From a deck of 52 cards find the probability of the fallowing -
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.

Answer 1

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%