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Chapter 15: Q23P (page 744)
Do Problem if one person is busy evenings, one is busyevenings, two are each busy one evening, and the rest are free every evening.
The required probability is .
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A letter is selected at random from the alphabet. What is the probability that it is one of the letters in the word “probability?” What is the probability that it occurs in the first half of the alphabet? What is the probability that it is a letter after x?
A single card is drawn at random from a shuffled deck. What is the probability that it is red? That it is the ace of hearts? That it is either a three or a five? That it is either an ace or red or both?
A so-called 7-way lamp has three 60-watt bulbs which may be turned on one or two or all three at a time, and a large bulb which may be turned to 100 watts, 200 watts or300 watts. How many different light intensities can the lamp be set to give if the completely off position is not included? (The answer is not 7.)
Some transistors of two different kinds (call them N and P) are stored in two boxes. You know that there are 6 N’s in one box and that 2 N’s and 3 P’s got mixed in the other box, but you don’t know which box is which. You select a box and a transistorfrom it at random and find that it is an N; what is the probability that it came from the box with the 6 N’s? From the other box? If another transistor is picked from the same box as the first, what is the probability that it is also an N?
Let be independent random variables, each with density function , expected value , and variance . Define the sample meanby.Showthat,and . (See Problems and.)
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