Addition Rules for Probability Mutually Exclusive Events When do you add/ when do you subtract probabilities?

Mutually Exclusive Events Two events are considered mutually exclusive if they cannot occur at the same time on a single trial. No outcomes in common. Examples: heads/tails Odd #/Even # 2 or 3 in deck of cards Red or black card

Mutually Exclusive Events When 2 events A and B are mutually exclusive the probability that either A or B will occur on a single trial is: P(A or B) = P(A) + P(B) Example 1: A bag contains 3 red, 2 blue and 5 green balls. A single ball is drawn from the bag. Find the probability of selecting either a red or green ball. P(R or G) = P(R) + P(G)

Example 2: Mutually Exclusive In a recent year, 45% of voters in PA were registered Democrat, 40% were registered Republican and 15% were registered Independent. Find the probability that if a voter is selected at random, he is registered either Republican or Independent. P(R or I) = P(R) + P(I) =40% + 15% = 55%

Non-Mutually Exclusive Events Two events are not mutually exclusive if it is possible for the events to occur at the same time on a single trial. Have at least one outcome in common. Examples: 3 or odd # Jack or red card female or senior

Non-Mutually Exclusive Events When 2 events A and B are not mutually exclusive the probability that either A or B will occur on a single trial is: P(A or B) = P(A) + P(B) – P(A and B) Example 1: A Card is drawn from a standard deck of cards. Find the probability of selecting either a 2 or a heart. P(2 or H) = P(2) + P(H) – P(2 and H)

Example 2: Non-Mutually Exclusive A study of patient records at a public health clinic showed that 15% of the patients had a dental exam, 45% had a general physical and 5% had both. If a patient’s record is randomly selected, what is the probability that the patient received either a dental exam or a physical? P(D or P) = P(D) + P(P) – P(D and P) =15% + 45% - 5% = 55%

Other Examples 1 The probability that a customer at an ice cream shop selects sprinkles or hot fudge is.43, and the probability that the customer selects sprinkles only is.32. If the probability that he or she selects hot fudge only is.17, find the probability of the customer selecting both items. P(S or F) = P(S) + P(F) – P(S and F).43 = – P(S and F).06= P(S and F)

Other Examples 2 The Bargain Auto Mall has these cars in stock. If a car is selected at random, find the probability that it is a. Domestic b. Foreign and Mid-size c. Domestic or an SUV SUVCompactMid-Sized Foreign Domestic

Solution – Other Example 2 Sample space = 300 a)P(D) = 210/300 b)P(F and M) = 20/300 c)P(D or an SUV) = 230/300 SUVCompactMid-Sized Foreign Domestic