Probability of the Union of Mutually Exclusive Events

When two events (call them "A" and "B") are Mutually Exclusive. It is impossible for them to happen together:

P(A and B) = 0

"The probability of A and B together equals 0 (impossible)"

The probability of A or B is the sum of the individual probabilities:

P(A U B) = P(A) + P(B)

Example1: What is the probability of drawing a queen or a king on an ordinary deck of cards?

P(queen or king) = P(queen) + P(king)

P(queen) = 13/52 = 1/4

P(king) = 13/52 = 1/4

P(queen or king) = 1/13 + 1/14 

= 2/13

Example 2: A bag contains 7 white balls, 11 orange balls and 12 redbballs. If a ball is drawn, find the probability that it is a white or a red ball.

P(white or red) = P(white) + P(red)

P(white) = 7/30

P(red) = 12/30

P(white or red) = 7/30 + 12/30 

= 19/30

Example 3: A card is drawn at random from a 52 - deck of card. Find the Probability of getting:

a. a king or an ace?

b. a number card or an ace?

c. a black card or a diamond?

d. a red card or a club?

e. a king or an odd number?

Solution:

a. A king or an ace!

4/52 + 4/52 = 8/52 = 2/13 

b. a number card or an ace!

36/52 + 4/52 = 40/52= 10/13

c. a black card or a diamond?

26/52 + 13/52 = 39/52 = 1/4 

d. a red card or a club?

26/52 + 13/s2 =39/52 = 1/4 

e. a king or an odd number?

4/52+ 16/52 = 20/52 =5/13