'50. The odds that a delivery service will deliver a package by noon tomorrow are 9 to 1. A What is the probability that the package will arrive by noon tomorrow? B. What is the probability that the package will not arrive by noon tomorrow?'
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Key Concepts
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Refer to the previous exercise. Suppose that 50$\%$ of the overnight parcels are sent via express mail service $E_{2}$ and the remaining 10$\%$ are sent via $E_{3} .$ Of those sent via $E_{2},$ only 1$\%$ arrive late, whereas 5$\%$ of the parcels handled by $E_{3}$ arrive late. (a) What is the probability that a randomly selected parcel arrived late? (b) If a randomly selected parcel has arrived on time, what is the probability that it was not sent via $E_{1}$ ?
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A particularly long traffic light on your morning commute is green on $20 \%$ of the mornings. Assume that each morning represents an independent trial. (a) What is the probability that the first morning that the light is green is the fourth morning? (b) What is the probability that the light is not green for 10 consecutive mornings?
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