A company places a rush order for wire of two thicknesses. Consignments of each thickness are to be sent immediately when they are available. Previous experience suggests that the probability is 0.8 that at least one of these consignments will arrive within a week. It is also estimated that, if the thinner wire arrives within a week, the probability is 0.4 that the thicker wire will also arrive within a week. Further, it is estimated that, if the thicker wire arrives within a week, the probability is 0.6 that the thinner wire will also arrive within a week.a. What is the probability that the thicker wire will arrive within a week?b. What is the probability that the thinner wire will arrive within a week?c. What is the probability that both consignments will arrive within a week?

An insurance company found that 2.4% of male drivers between the ages of 18 and 25 are involved in serious accidents annually. To simplify the analysis, assume that every such accident costs the insurance company $62,000 and that a driver can only have one of these accidents in a year. Complete parts (a) through (c). (a) If the company charges $2,600 for such coverage, what is the chance that it loses money on a single policy? P(loses money)= .024 (Type an integer or a decimal.) (b) Suppose that the company writes 1,000 such policies to a collection of drivers. What is the probability that the company makes a profit on these policies? Assume that the drivers don't run into each other and behave independently. P(profit) = .976 (Round to five decimal places as needed.)

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a​ student's alarm clock has a 16.5​% daily failure rate. a. What is the probability that the​ student's alarm clock will not work on the morning of an important final​ exam? ​(Round to three decimal places as​ needed.)   b. If the student has two such alarm​ clocks, what is the probability that they both fail on the morning of an important final​ exam?   ​(Round to five decimal places as​ needed.)   c. What is the probability of not being awakened if the student uses three independent alarm​ clocks?   ​(Round to five decimal places as​ needed.)

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a​ student's alarm clock has a 5.6​% daily failure rate. Complete parts​ (a) through​ (d) below. a. What is the probability that the​ student's alarm clock will not work on the morning of an important final​ exam?     b. If the student has two such alarm​ clocks, what is the probability that they both fail on the morning of an important final​ exam?     c. What is the probability of not being awakened if the student uses three independent alarm​ clocks?     d. Do the second and third alarm clocks result in greatly improved​ reliability?     A. ​No, because the malfunction of both is equally or more likely than the malfunction of one.   B. ​No, because total malfunction would still not be unlikely.   C. ​Yes, because total malfunction would not be​ impossible, but it would be unlikely.   D. ​Yes, because you can always be certain that at…