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Probabilities of Compound Events Probability of Two Independent Events If two events, A and B are independent, then the probability of both events occurring is the product of each individual probability. P(A and B) = P(A) * P(B)

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Probabilities of Compound Events Find the probability of drawing a face card, replacing the card and then drawing an ace using a standard deck of playing cards P(A)= 12/52 P(B)= 4/52 P(A and B) = 12/52 * 4/52 = 3/169

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Probabilities of Compound Events In a survey it was determined that 7 out of 10 shoppers do not use coupons and 3 out of 8 shoppers only buy items on sale. What is the probability that a random shopper will use a coupon and buy a item on sale. ( It has been determined that these two situations are independent.) P(A) = 1 - 7/10 = 3/10 P(B) = 3/8 P(A and B) = 3/10 * 3/8 = 9/80

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Probabilities of Compound Events Probability of Two Dependent Events If two events, A and B, are dependent, then the probability of both events occurring is the product of each individual probability. P(A and B) = P(A) * P(B following A)

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Probabilities of Compound Events In a bag there are 4 red, 6 green and 3 blue candies. Bob will pick 3 candies randomly from the bag (no replacement). Independent or dependent? What is the probability that Bob drew all blue candies? P(A, then B, then C) 3/13 * 2/12 * 1/11 = 1/286

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Probabilities of Compound Events Probability of Mutually Exclusive Events Mutually exclusive: When two events cannot happen at the same time If two events, A and B are mutually exclusive, then the probability that either A or B occurs is the sum of their probabilities P(A or B) = P(A) + P(B)

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Probabilities of Compound Events Betty has 6 pennies, 4 nickels and 5 dimes in her pocket. If Betty takes one coin out of her pocket, what is the probability that it is a nickel or a dime? P(A) = 4/15 P(B) = 5/15 P(A or B) = 4/15 + 5/15 = 9/15 = 3/5

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Probabilities of Compound Events Probability of Inclusive Events Mutually Inclusive: When two events can happen at the same time If Two events, A and B are inclusive, then the probability that either A or B occurs is the sum of their probabilities decreased by the probability of both events occurring. P(A or B) = P(A) + P(B) – P(A and B)

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Probabilities of Compound Events In a particular group of hospital patients, the probability of having high blood pressure is 3/8, the probability of having arteriosclerosis is 5/12, and the probability of having both is ¼. Mutually exclusive or inclusive? What is the probability that a patient has either HBP or arteriosclerosis?

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Probabilities of Compound Events There are 6 children in an art class, 4 girls and 2 boys. Four children will be chosen at random to act as greeters for an art exhibit. What is the probability that at least 3 girls will be selected?

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