A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting

· an even number ten or less given the card is a not a heart.
· a five given the card is a face card.
· an Ace, given that the card is red.

Show step by step work. Give all solutions exactly in reduced fraction form

Question

A card is selected from a standard deck of 52 playing cards. A standard deck of cards has 12 face cards and four Aces (Aces are not face cards). Find the probability of selecting
 
·         an even number ten or less given the card is a not a heart.
·         a five given the card is a face card.
·         an Ace, given that the card is red.
 
Show step by step work. Give all solutions exactly in reduced fraction form

anonymous · Answer

I'm assuming aces are high...

a) If it's not a heart, that leaves 39 cards possible. Of those, 12 are higher than 10 (3 Aces, K's, Q's, J's). This leaves 27 cards possible. Of those, 15 are even (3 each of 10's, 8's, 6's, 4's, 2's). So our answer is 15/52.

b) If it's a face card, can it be a five?

c) 26 red cards, two of them are aces. Answer is 2/26=1/13