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EXAMPLE 2

Racing. In a BMX meet, each heat consists of 8 competitors who are randomly assigned lanes from 1 to 8 . What is the probability that a racer will draw lane 8 in the 3 heats in which the racer participates?. 1. 1. 1. P ( A and B and C ). = P ( A ) P ( B ) P ( C ). =. 8. 8. 8.

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EXAMPLE 2

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  1. Racing In a BMX meet, each heat consists of 8 competitors who are randomly assigned lanes from 1 to 8. What is the probability that a racer will draw lane 8 in the 3 heats in which the racer participates? 1 1 1 P(A andB andC) = P(A)P(B)P(C) = 8 8 8 1 0.00195 = 512 EXAMPLE 2 Find probability of three independent events SOLUTION Let events A, B, and Cbe drawing lane 8 in the first, second, and thirdheats, respectively. The three events are independent. So, the probability is:

  2. Music While you are riding to school, your portable CD player randomly plays 4 different songs from a CD with 16 songs on it. What is the probability that you will hear your favorite song on the CD at least once during the week (5 days)? 15C4 P(not hearing song) = 16C4 EXAMPLE 3 Use a complement to find a probability SOLUTION For one day, the probability of not hearing your favorite song is:

  3. P(hearing song) = 1– [P(not hearing song)]5 ( ) 15C4 5 0.763 = 1– 16C4 EXAMPLE 3 Use a complement to find a probability Hearing or not hearing your favorite song on Monday, on Tuesday, and so on are independent events. So, the probability of hearing the song at least once is:

  4. SPINNER : A spinner is divided into ten equal regions numbered 1 to 10. What is the probability that 3 consecutive spins result in perfect squares? ANSWER 0.027 for Examples 2 and 3 GUIDED PRACTICE

  5. What If? In Example 3, how does your answer change if the CD has only 12 songs on it? ANSWER It increases to about 0.87. for Examples 2 and 3 GUIDED PRACTICE

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