258 Part 4: The State of the World
a black card? Start with the probability of drawing an ace. P ace 554
521
13. Then you want
the probability of drawing a black card: P black^26
52
1
2. Before you add, think for a minute.
There’s a little problem, or more accurately, two little problems: the ace of spades and the ace of
clubs. The probability of an ace was based on four aces, including the ace of spades and the ace
of clubs. The probability of a black card was based on 26 black cards, including the ace of spades
and the ace of clubs. The two black aces are being counted twice, so you’ll have to make an
adjustment for that.
In general, the probability of A or B is the probability of A plus the probability of B minus the
probability of A and B.
PPPBPA or B A A and B
You may wonder why this little adjustment wasn’t necessary in the example about rolling
the die. The answer is that when you roll a die, getting a five and getting a six are mutually
exclusive outcomes. There is no way that you can get a five and a six on the same roll.
When event A and event B are mutually exclusive, the probability of A and B is zero, so
PPPBPA or B A A and B just becomes PPPBA or B A.PPPPace or black ace black black ace
4
5226
522
52
228
527
13
CHECK POINT
A bag contains 24 marbles. Six of the marbles in the bag are red, 4 are blue, 3 are
white, 9 are green and 2 are yellow. One marble will be chosen at random.- What is the probability that the marble chosen is red or blue?
- What is the probability that the chosen marble is yellow or blue?
- What is the probability that the marble is green or white?
- What is the probability that the chosen marble is yellow or red?
- What is the probability that the marble is red or orange?