Ap Stats. HELP

Question 4 W Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. A shopping mall has three automated teller machines (ATMs). Because the machines receive heavy use, they sometimes stop working and need to be repaired. Let the random variable X represent the number of ATMs that are working when the mall opens on a randomly selected day. The table shows the probability distribution of X. Number of ATMs working when the mall opens 0 2 3 Probability 0.15 0.21 0.40 0.24 a. What is the probability that at least one ATM is working when the mall opens? b. What is the expected value of the number of ATMs that are working when the mall opens? c. What is the probability that all three ATMs are working when the mall opens, given that at least one ATM is working? d. Given that at least one ATM is working when the mall opens, would the expected value of the number of ATMs that are working be less than, equal to, or greater than the expected value from part (b) ? Explain.Question 5 W Directions: Show all your work. Indicate clearly the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy of your results and explanation. An airline claims that there is a 0.10 probability that a coach-class ticket holder who flies frequently will be upgraded to first class on any flight. This outcome is independent from flight to flight. Sam is a frequent flier who always purchases coach-class tickets. a. What is the probability that Sam's first upgrade will occur after the third flight? b. What is the probability that Sam will be upgraded exactly 2 times in his next 20 flights? c. Sam will take 104 flights next year. Would you be surprised if Sam receives more than 20 upgrades to first class during the year? Justify your