SOLUTION: A card is selected from a standard deck of 52 playing cards. Find the probability of selecting 1. a five given the card is a not a club. 2. a heart given the card is red.

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Question 325317: A card is selected from a standard deck of 52 playing cards. Find the probability of selecting
1. a five given the card is a not a club.
2. a heart given the card is red.
3. a face card, given that the card is black. (An ace is not a face card.)
Show step by step work. Give all solutions exactly in reduced fraction form.
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A card is selected from a standard deck of 52 playing cards. Find the probability of selecting
1. a five given the card is a not a club.

Since you are given that it is not a club, then you are drawing from a deck of
only 39 cards with no clubs, just hearts, diamonds and spades.  In such a deck,
there are 3 fives.  That's 3 out of 39, so the probability is 3%2F39 or
reducing you get 1%2F13.


2. a heart given the card is red.

Since you are given that it is red, then you are drawing from a deck of only 26
cards with no spades or clubs, just hearts and diamonds.  In such a deck,
there are 2 fives.  That's 2 out of 26, so the probability is 2%2F26 or
reducing you get 1%2F13.

3. a face card, given that the card is black. (An ace is not a face card.) 

Since you are given that it is black, then you are drawing from a deck of only
26 cards with no hearts or diamonds, just spades and clubs.  In such a deck,
there are 6 face cards, the J,Q and K of spades and the J,Q, and K of clubs. 
That's 6 out of 26, so the probability is 6%2F26 or reducing you get
3%2F13.

Edwin