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1、13.4 Find Probabilities Using Combinations,Students will use combinations to count possibilities.Students will do assigned homework.Students will study vocabulary words.,Lesson 13.4, For use with pages 861-867,Find the product.,Lesson 13.4, For use with pages 861-867,Find the product.,Lesson 13.4, F
2、or use with pages 861-867,Find the product.,Daily Homework Quiz,For use after Lesson 13.3,Daily Homework Quiz,For use after Lesson 13.3,EXAMPLE 1,Find the probability of A or B,You roll a number cube. Find the probability that you roll a 2 or an odd number.,SOLUTION,Because 2 is an even number, roll
3、ing a 2 and rolling an odd number are mutually exclusive events.,P(2 or odd) = P(2) + P(odd),EXAMPLE 2,Find the probability of A or B,You roll a number cube. Find the probability that you roll an even number or a prime number.,SOLUTION,Because 2 is both an even number and a prime number, rolling an
4、even number and rolling a prime number are overlapping events. There are 3 even numbers, 3 prime numbers, and 1 number that is both.,P(even or prime) = P(even) + P(prime) P(even and prime),GUIDED PRACTICE,for Examples 2 and 3,1. You roll a number cube. Find the probability that you roll a 2 or a 5.,
5、2. You roll a number cube. Find the probability that you roll a number less than 4 or an odd number.,EXAMPLE 3,Find the probability of A and B,You take a city bus from your neighborhood to a location within walking distance of your school. The express bus arrives at your neighborhood between 7:30 an
6、d 7:36. The local bus arrives at your neighborhood between 7:30 and 7:40. You arrive at the bus stop at 7:33. Find the probability that you have missed both the express bus and the local bus.,BUS SCHEDULE,SOLUTION,The events are independent. The arrival of one bus does not affect the arrival of the
7、other bus.,EXAMPLE 3,Find the probability of A and B,There are 6 minutes whenthe express bus can arrive.You are not at the bus stopfor 3 of those minutes.,There are 10 minutes whenthe local bus can arrive.You are not at the bus stopfor 3 of those minutes.,P(you miss express bus),P(you miss local bus
8、),EXAMPLE 3,Find the probability of A and B,P(you miss both buses),Multiply the probabilities of the two events:,EXAMPLE 4,Find the probability of A and B,A box contains 3 blue pens and 5 black pens. You choose one pen at random, do not replace it, then choose a second pen at random. What is the pro
9、bability that both pens are blue?,PEN COLORS,SOLUTION,Because you do not replace the first pen, the events are dependent. Before you choose a pen, there are 8 pens, and 3 of them are blue. After you choose a blue pen, there are 7 pens left and 2 of them are blue.,P(blue and then blue) = P(blue) P(blue given blue),GUIDED PRACTICE,for Examples 3 and 4,3. MARBLES A bag contains 4 red, 5 green, and 2 blue marbles. You randomly draw 2 marbles, one at a time. Find the probability that both are red if:,a. You replace the first marble.,b. You do not replace the first marble.,
