probability
posted by alex on .
consider the experiment of selecting a card from an ordinary deck of 52 playing cards and determine the probability of the stated event.
A card that is not a king and not a spade is drawn.
I know there are 52 cards in a deck and there are 4 kings to a deck. And 13 spades in a deck. So I added the two together which would make it 17/52= 33% is this correct?

ahh, but you counted the "king of spades" twice.
there are only 12 cards that are NOT either kings or spades.
So you would be interested in drawing any of the other 40 cards
Prob(not a king and not a spade) = 40/52 = 10/13 
This is wrong!! Spades are ace through K which is 13 plus the other 3 kings which is 16, not twelve.

When a card is selected from a deck, find the probability of getting a king

4 Kings in deck of 52
4/52
13 spades 52
13/52
4/52 + 13/52 but remember the king is used twice so you have to take away the king in the spades which gives you:
4/52+12/52=16/52
But you problem is stating:
NOT A KING OR NOT A SPADE
So you have to SUBTRACT 1
P(E)= 1P(E)
So you get
P=(NOT A KING OR NOT A SPADE)
116/52=9/13