ASAP please. I need number 17 please 76 Chapter 2 Conditional Probability 14. Co
ID: 3146669 • Letter: A
Question
ASAP please. I need number 17 please 76 Chapter 2 Conditional Probability 14. Consider again the conditions of Exercise 13. If 10 particles are emitted, what is the probability that at least one of the particles will penetrate the shield? 20. Suppose that A:--… A1 form a scquence of k inde. pendent events. Let B··· be another sequence of k events such that for cach value of J U = L . . . . k), either B, = A, or B, = A, Prove that B-....8. are also inde- pendent events Hit Use an induction argument based on the number of events B, for whichBA 15. Consider again the conditions of Exercise 13. How many particles must be emitted in order for the probability to be at least 08 that at least one particle will penetrate the shield? 21. Prove Thoorem 2 22 on pagc 71. Hint The "only if 16. In the World Series of baseball, two teams A and Bdirection is direct from the definition of independence on play a sequence of games against each other, and the fist Page team that wins a total of four of the World Series If the probability that team A w let 1= 1 with =ir win any particular game against team B is 1 what is the probability that team A will win the World Series? 68. For the "if direction, use induction on the value becomes the winner o in the definition of independence. Let m j-I and games 22 Prove Theorem 22.4 on page 73 17. Two boys A and B throw a ball at a target. Suppose 2*. A programmer is about to attempt to compile a se- that the peobability that boy A will hit the target on any ries of 11 similar programs Let A throw is 1/3 and the probability that boy B will hit the ith program comples successfully for i =L 11. when target on any throw is 1/4. Suppose also that boy A throwsthe programming task is eass, the programmer expects first and the two boys take turns throwing Determine the hat s0 percent of programs should compile. When the probability that the target will be hit for the first time on programming task is difticult, she expects that only 4oper- the third throw of boy A Let A, be the event that the cent of the programs will compile. Let B be the event that the peogramming task was casy The programmer believes 18. For the conditions of Exercise 17, determine the prob-that the events A.....Anare conditionally independent ability that boy A will hit the target before boy B does given B and given B 19. A box contains 20 red balls, 30 white balls, and 50 a. Compute the probability that exactly 8 out of 11 blue balls Suppose that 10 balls are selected at random one at a time, with replacement: that is, each selected ball . Compute the probability that exactly 8 out of 11 is replaced in the box before the next selection is made Determine the probability that at least one color will be missing from the 10 selected balls programs will compile given B programs will compile given 24. Prove Theorem 223 on page 72. 2.3 Bayes' Theorem Suppose that we are interested in which of several disjoint events By....B will occur and that we will get to observe some other event A. If Pr(A|B)is available for each i.hen Bayes, theorem is a usefl formula for computing the conditional probabilities of the B, events given A We begin with a typical example Example Test for a Disease. Suppose that you are walking down the street and notice that the 23. Department of Public Health is giving a free medical test for a certain disease. The test is 90 percent reliable in the following sense: Ií a person has the disease, there is a prohability of 09 that the test will give a positive response: whereas if a person does not have the disease, there is a probability of oaly 0.1 that the test will give a positive Data indicate that your chances of having the disease are only 1 in 10,000 However, since the test costs you nothing, and is fast and harmless, you decide to stop and take the test. A few days later you learn that you had a positive response to the test. Now, what is the probability that you have the disease?Explanation / Answer
You want a series of independent event so occur, so you just multply
the probability of each event.
You want misses followed by a hit so that would be
2/3 x 3/4 x 2/3 x 3/4 x 1/3 = .083333