Mutually exclusive events are two or more events that cannot occur simultaneously. If one die is thrown and comes up three, it cannot come up six or any other number at the same time. If a coin is tossed and comes up tails, it cannot come up heads on the same toss. If a person weighs 125 pounds, he cannot have any other weight simultaneously.
The probability of one or the other of two mutually exclusive events happening is the sum of the separate probabilities of these events. If X and Y represent two mutually exclusive events
P(X or Y) = P(X) + P(Y)
This is known as the addition theorem and may be extended to any number of mutually eXclusive events.
If a bag contains four blue marbles, six yellow marbles, and five green marbles, what is the probability that in one drawing a person will pick either a blue marble or a green marble?
There are fifteen marbles in the bag. The probability that a blue marble will be selected is 4/15. The probability that a green marble will be drawn is 5/15 or 1/3.
P(B or G)—P(B) + P(G) = 4/15 + 5/15 = 9/15 = 3/5
The probability that either a blue marble or a green marble will be drawn is 3/5.
If a die is thrown, what is the probability that either a two or a six will come up?
The die can come up any one of six ways. The probability that a two will come up is 1/6. The probability that a six will come up is 1/6.
P(2 or 6) = P(2) + P(6) = 1/6 + 1/6 = 2/6 = 1/3
The probability that either a two or a six will come up is 1/3.
1.) Are the following pairs of events mutually exclusive?
a.) Living in New Haven and working in New York.
b.) Being a freshman and being a junior in high school.
c.) Being a professor and being an author of a book.
d.) Drawing a red card and drawing the ace of spades.
e.) Drawing a face card and drawing the six of hearts from a normal deck of cards.
2.) If the probabilities that Joan, Beverly and Evelyn will be elected secretary of a ski club are 1/8, 2/5, and 1/3 respectively, find the probability that one of the three will be elected.
3.) If the probabilities that John and Harry will be valedictorian of a high school class are 1/4 and 3/7 respectively, what is the probability that either John or Harry will be valedictorian?
4.) Chris and Janet are among twenty girls who enter a tennis tournament. What is the probability that either one of these two girls will win the tournament?
5.) In a drawer are six white gloves, four black gloves, and eight brown gloves. If a glove is picked at random, what is the probability that it will be either white or brown?