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Probability of Multiple Events (Independent and Dependent Events)

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Presentation transcript:

Warm Up

L9-6 Obj: Students will solve rational equations

Solve = . Check each solution. Solving Rational Equations Solve = . Check each solution. 1 x – 3 6x x 2 – 9

Solve

Solve

3 5x 4 3x 1 3 Solve – = .

Solve

time to row 4 miles upstream = time to row 6 miles downstream Josefina can row 4 miles upstream in a river in the same time it takes her to row 6 miles downstream. Her rate of rowing in still water is 2 miles per hour. Find the speed of the river current. Relate: speed with the current = speed in still water + speed of the current, speed against the current = speed in still water – speed of the current, time to row 4 miles upstream = time to row 6 miles downstream Define: Distance (mi) Rate (mi/h) Time (h) With current 6 2 + r Against current 4 2 – r 4 (2 – r ) 6 (2 + r ) Write: = 6 (2 + r ) 4 (2 – r )

White Board Graph Simplify

L9-7 Obj: Students will find probabilities of events A and B Events are Independent if they do not affect each other. Events are dependent if one event is affected by the other event.

Classify each pair of events as dependent or independent. Probability of Multiple Events LESSON 9-7 Additional Examples Classify each pair of events as dependent or independent. a. Spin a spinner. Select a marble from a bag that contains marbles of different colors. b. Select a marble from a bag that contains marbles of two colors. Put the marble aside, and select a second marble from the bag.

Are the events mutually exclusive? Explain. a. rolling an even number and rolling a number greater than 5 on a number cube b. rolling a prime number or a multiple of 6 on a number cube

Relate: probability of both events is probability of first event Probability of Multiple Events LESSON 9-7 Additional Examples A box contains 20 red marbles and 30 blue marbles. A second box contains 10 white marbles and 47 black marbles. If you choose one marble from each box without looking, what is the probability that you get a blue marble and a black marble? 30 50 47 57 Relate: probability of both events is probability of first event times probability of second event Define: Event A = first marble is blue. Then P(A) = . Event B = second marble is black. Then P(B) = . Write: P(A and B) = P(A) • P(B)

What is the probability that a customer will choose beans or spinach? Probability of Multiple Events At a restaurant, customers get to choose one of four vegetables with any main course. About 33% of the customers choose green beans, and about 28% choose spinach. What is the probability that a customer will choose beans or spinach? A spinner has twenty equal-size sections numbered from 1 to 20. If you spin the spinner, what is the probability that the number you spin will be a multiple of 2 or a multiple of 3?

Practice Problems

If the probability of Timmy trying out for track is 20% and if he does the probability of him running the 400m is 40%. What is the probability he joins track and does not run the 400m?

Practice Homework L9.7 (page 542) 2-44e HW: L9-6 (p 532) #6-28e 40-44e 62-70e L9.7 (page 542) 2-44e

Review Solve for x 7x = 15

Review Solve for x log (2x – 1) = 2

Review Solve for x log (5x- 2) = 3

Review Solve for x 112x = 37