Addition Rules of Probability OBJECTIVE Recognize Mutually Exclusive

Addition Rules of Probability……

OBJECTIVE ¡Recognize Mutually Exclusive Events ¡Use the Addition Rule of Probability

RELEVANCE To find the likelihood of an event occurring by observing the longterm proportion in which a certain outcome is observed.

Card Facts…… 1. 2. 3. 4. 5. 52 cards in the deck 4 suits 13 cards in each suit (diamond, hearts, clubs, spades) Face cards – jack, queen, king 26 red cards; 26 black cards

Mutually Exclusive Events…… ¡ ¡ Events that cannot occur at the same time. For example: Being a junior and being a senior are mutually exclusive.

Determine which events are mutually exclusive when a single die is rolled…. . 1. 2. 3. 4. 5. Getting a 4 and a 6 Getting an odd # and an even # Getting an odd# and a # less than 4 Getting a # greater than 4 and a # less than 4 Getting a 3 and an odd # 2. Mutually Exclusive 3. Not M. E. 4. Mutually Exclusive 5. Not M. E. 1.

You Try…Which are mutually exclusive when a single card is drawn from a deck? . . . 1. 2. 3. 4. Getting a 7 and J Getting a club and king Getting a face card an ace Getting a face card and a spade 2. M. E Not M. E. 3. M. E. 4. Not M. E. 1.

Addition Rule – M. E. Events…… ¡ When 2 events are mutually exclusive, the probability that A or B will occur is

Example…… ¡ A box contains 3 glazed, 4 jelly, and 5 chocolate doughnuts. If a person selects one doughnut at random, find the probability that it is either glazed or chocolate.

Answer…… ¡ ¡ Sample Space = 3+4+5 = 12 doughnuts P(glazed or choc) = P(glazed) + P(chocolate)

Example…… ¡ At a political rally, there are 20 republicans, 13 democrats, and 6 independents. If a person is selected at random, find the probability that he or she is either a democrat or an independent.

Answer…… ¡ Sample Space = 20+13+6=39 ¡ P(dem or ind) = P(dem)+P(ind)

Example…… ¡ A day of the week is selected at random. Find the probability that it is a day of the weekend.

Answer…… ¡ Sample Space = 7 days in a week P(Sat or Sun)= P(Sat) + P(Sun)

Addition Rule – NOT Mutually Exclusive…… ¡ ¡ When 2 events are NOT mutually exclusive, the probability that A or B will occur is The Formal Addition Rule

Example…… ¡ A single card is drawn from a deck. Find the probability that it is a king or club.

Example…… In a hospital unit there are 8 nurses and 5 doctors. 7 nurses and 3 doctors are female. If a staff person is selected, find the probability that the subject is a nurse or a male. ¡ Suggestion: Make a contingency table. ¡

Find the P(nurse or male) ¡ ¡ Females Males Total Nurse 7 1 8 Doctors 3 2 5 Total 10 3 13 Let n = nurse and m = male P(n or m) = P(nurse) + P(m) – P(nurse and male)

Example…… ¡ On New Year’s Eve, the probability of a person driving while intoxicated is 0. 32, the prob. of a person having an accident is. 09, and the prob. of a person having an accident while intoxicated is. 06. What is the probability of a person driving while intoxicated or having an accident?

Answer…… ¡ P(intox or acc) = P(intox) + P(acc) – P(intox and acc)