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Sec. 3.3 β The Addition Rule Two events A and B are ________________ _______________ if A and B cannot occur at the same time. Decide whether or not the events are mutually exclusive. Event A: Roll a 3 on a die. Event B: Roll a 4 on a die. Event A: Randomly select a male student. Event B: Randomly select a nursing major. Event A: Randomly select a blood donor with type O blood. Event B: Randomly select a female blood donor. The Addition Rule The probability that events A or B will occur, π(π΄ ππ π΅), is given by __________________________________ If events A and B are mutually exclusive the rule can be simplified to __________________________________ Find the probabilities of the following events. You select a card from a standard deck. a. Find the probability that the card is a 4 or an ace. b. Find the probability that the card is a diamond or a 7. c. Find the probability that the card is a red suit or a queen. d. Find the probability that the card is a 3 or a face card. You roll a six-sided die. a. Find the probability of rolling a number less than three or rolling an odd number. b. Find the probability of rolling a 6 or a number greater than 4. c. Find the probability of rolling a number less than 5 or an odd number. d. Find the probability of rolling a 3 or an even number. A college has an undergraduate enrollment of 3500. Of these 860 are business majors and 1800 are women. Of the business majors, 425 are women. If a college newspaper conducts a poll and selects students at random to answer a survey, find the probability that a selected student is a woman or a business major. The table shows the results of a survey t hat asked 3203 people whether they wear contacts or glasses. A person is selected at random from the sample. Find the probability of each event. Male Female Total Contacts Only 64 189 253 Glasses Only 841 427 1268 Both Glasses and Contacts 177 368 545 Neither 456 681 1137 a. The person wears contacts only or glasses only. b. The person is male or wears both contacts and glasses. c. The person is female or wears neither contacts nor glasses. d. The person is male or does not wear glasses. Total 1538 1665 3203 Type of Probability and probability rules In words The number of outcomes in the sample space is known and each outcome is equally likely to occur. The frequency of outcomes in the sample space is estimated from experimentation. The probability of an event is between 0 and 1, inclusive. The complement of event E is the set of all outcomes in a sample space that are not included in πΈ, denoted by πΈβ². The Multiplication Rule is used to find the probability of two events occurring in a sequence. The Addition Rule is used to find the probability of at least one of two events occurring. In symbols