Answer:
7/13
Step-by-step explanation:
If we are looking at a standard deck of playing cards, we have 52 cards total.
*13 of each suit (there are 4 suits; spades, clubs, hearts, and diamonds)
*2 kinds of colors-black or red. Half the deck is black and half the deck is red. There are 26 reds and 26 blacks.
*There is 1 king of each suit and since there are 4 suits, then there are 4 kings.
We can make other observations.
P(King or black card)
=P(King)+P(black card)-P(king and black card)
(We are subtracting out anything that counted twice in the "and" part)
=4/52 + 26/52 - 2/52
Notes:
-P(king)=4/52 comes from there being 4 kings in all in a deck of 52 playing cards.
-P(black card)=26/52 comes from that half the deck is black (and the other half is red) in a deck of 52 playing cards. Technically, we could have just said this equal 1/2 here instead. I will leave as 26/52 for now so I can have a common denominator already setup.
-P(king and black card)=2/52 comes from there being 2 black cards that are kings in a deck of 52 playing cards. We have to get rid of these 2 from the 4+26 since if we don't we would have counted them twice)
Let's simplify:
=(4+26-2)/52
=(30-2)/52
=28/52
Let's reduce:
=(28/4)/(52/4)
=7/13
