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Secretary types

1. A secretary types three letters and the three corresponding envelopes. In a hurry, he places at random one letter in each envelope. What is the probability that at least one letter is in the correct envelope? 2. Consider poker hands drawn from a well-shuffled deck as described in Example 1.3.4. Determine the probability of

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The experiment

Suppose the experiment is to choose a real number at random in the interval (0, 1). For any subinterval (a, b) ⊂ (0, 1), it seems reasonable to assign the probability P[(a, b)] = b−a; i.e., the probability of selecting the point from a subinterval is directly proportional to the length of the subinterval. If

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Prove expression

Prove expression (1.3.9). Consider Remark 1.3.2. (b) Now prove the general inclusion exclusion formula given by the expression (1.3.13). 1.3.13 Three distinct integers are chosen at random from the first 20 positive integers. Compute the probability that: (a) their sum is even; (b) their product is even.

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Effects of technology in education:Limiting social media to teenagers

These assignment focuses on the  effects of using technology in education. Further explain factor that lead to limiting social media to teenagers. Effects of technology in education:Limiting social media to teenagers Choose one of the following topics to write on the causes OR the effects (these are two different things). Some of the topics are

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The target

Each of four persons fires one shot at a target. Let denote the event that the target is hit by person compute the probability that (a) all of them hit the target; (b) exactly one hits the target; (c) no one hits the target; (d) at least one hits the target.

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The first trial

A bowl contains three red (R) balls and seven white (W) balls of exactly the same size and shape. Select balls successively at random and with replacement so that the events of white on the first trial, white on the second, and so on, can be assumed to be independent. In four trials, make certain

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