750 CHAPTER 11 Probability b) We want to determine the probability that 4 of 4 college students randomly selected will work during spring break. Thus, x 4 = and n 4. = We wish to determine P(4). = = = = = − − P x C p q P C ( ) ( ) (4) ( )(0.2) (0.8) 1(0.2) (0.8) 1(0.0016)(1) 0.0016 n x x n x 4 4 4 4 4 4 0 Thus, the probability that exactly 4 of 4 randomly selected college students will work during spring break is 0.0016. 7 Now try Exercise 19 Example 4 Planting Trees The probability that a tree planted by Forever Green Landscaping will survive is 0.8. Determine the probability that a) none of four trees planted will survive. b) at least one of four trees planted will survive. Solution a) Success is a tree that survives. Thus, p 0.8 = and q p 1 1 0.8 0.2. = − = − = We want to determine the probability of 0 successes in 4 trials. Thus, x 0 = and n 4. = We determine the probability of 0 successes, or P(0), as follows. = = = = = − − P x C p q P C ( ) ( ) (0) ( )(0.8) (0.2) 1(1)(0.2) 1(1)(0.0016) 0.0016 n x x n x 4 0 0 4 0 4 Thus, the probability that none of the four trees planted will survive is 0.0016. b) In Section 11.4, we introduced the formula: P P (event happening at least once) 1 (event does not happen). = − In part (a), we determined the probability that none of the four trees planted survives is 0.0016. Thus, P P (at least one tree planted will survive) 1 none of the four trees planted will survive 1 0.0016 0.9984 = − ⎛ ⎝⎜ ⎞ ⎠⎟ = − = 7 Now try Exercise 17 Learning Catalytics Keyword: Angel-SOM-11.10 (See Preface for additional details.) Instructor Resources for Section 11.10 in MyLab Math • Objective-Level Videos 11.10 • StatCrunch: Simulation: Urn Sampling • StatCrunch: Simulation: Dice Rolling • PowerPoint Lecture Slides 11.10 • MyLab Exercises and Assignments 11.10 • Chapter 11 Projects
RkJQdWJsaXNoZXIy NjM5ODQ=