One card is selected from an ordinary deck of 52. Find the probability as a common fraction in simplest form for each event below: __a face card __A heart and a diamond __A spade card and a quees __ a blake ace or five __a club, a diamond or a king __a black card or a red card
__a face card
So, there are 3 face cards per suit (jack, queen, king), and 4 suits. So there will be 3*4 = 12 face cards in a deck of 52.
12/52 = 3/13
__A heart and a diamond
So, this question is asking the probability of drawing a card that is both an ace AND a diamond. There is only 1 card in the deck that is both (an ace of diamonds), so this fraction would simply be 1/52.
__A spade card and a queen
Similarly, only one card in a deck can be both a spade AND a queen (a queen of spades). Again, this fraction would be 1/52.
__ a black ace or five
Now, this is asking about ORs. We will have to find all the black aces and all of the fives in the deck. There are only the ace of spades and ace of clubs that would be a black ace. All 4 suits of five could be picked though. Because this is asking about an OR we will be adding the probabilities of these together. 2/52 + 4/52 = 6/52. Simplified, this will be 3/26.
__a club, a diamond or a king
This one is a bit trickier. So the probability of picking a club or a diamond would just be 26/52. (13 clubs and 13 diamonds). And there will be 4 kings in a deck. BUT!!! We already accounted for the king of clubs and the king of diamonds, so we will only add 2/52 to the probability for the king of spades and the king of hearts.
This will be 13/52 + 13/52 + 2/52 = 28/52. Simplified this will be 7/13
__a black card or a red card
This one should be very easy. Isn’t a deck of cards made up of just black and red cards? 26 black cards and 26 red cards? The probability of picking a black or a red card would be 26/52 + 26/52 = 52/52, or 100%