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P.O.D. #7 basic In how many ways can a president, vice president, and secretary be randomly selected from a class of 25 students? Pres. VP Sec. Total 25 × 24 × 23 = 13,000 advanced A garage door code has 5 digits. If no digit is repeated, how many codes are possible? 1st 2nd 3rd 4th 5th 10 × 9 × 8 × 7 × 6 = 30,240 Independent & Dependent Events Independent events are two or more events in which the outcome of one event does not affect the outcome of the other event(s). Example: You roll a number cube twice. Dependent events are two or more events in which the outcome of one event affects the outcome of the other event(s). Example: You pick one card from a deck of playing cards, do not replace it, then pick another card. The probability of two independent events can be found by multiplying the probability of the first event by the probability of the second events. P(A B) = P(A) P(B) Example: A game requires players to roll two number cubes to move the game pieces. What is the probability of rolling a 3 or 4 on the first number cube and then rolling a 5 on the second? 2 1 P(3 or 4) = = 6 3 1 P(5) = 6 1 1 1 P( 3 or 4 AND 5) = = 3 6 18 The probability of two dependent events can be found by multiplying the probability of the first event by the probability of the second event after the first occurs. P(A B) = P(A) P(B following A) Example: What is the probability of picking a red card from a deck of playing cards, not returning it, and then picking a second red card? 26 1 P(first card is red) = = 52 2 25 P(second card is red) = 51 1 25 25 P(two red) = = 2 51 102 Whiteboard: A carnival game wheel has 12 equal sections. One of the sections contains a star. To win a prize, players must land on the section with the star on two consecutive spins. What is the probability of a player winning? P(1st 1 star) = 12 P(2nd 1 star) = 12 1 1 1 P(two stars) = = 12 12 144 Whiteboard: There are 4 oranges, 7 bananas, and 5 apples in a fruit basket. Dymond selects a piece of fruit at random. Then Yair selects a piece of fruit at random. Find the probability that two apples are chosen. 5 P(first piece is an apple) = 16 4 P(second piece is an apple) = 15 5 4 20 1 P(two apples) = = = 16 15 240 12