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Unformatted text preview: 0.1 Exercises for Chapter 2 1. Consider the experiment that measures the rise time of a reactor (in minutes and fractions of minutes). Let the sample space be the positive real numbers ( S = { x  x &gt; } ). Define the events A and B as follows, A = { x  x &lt; 72 . 5 } , and B = { x  x &gt; 52 . 5 } . Describe each of the events: (a) A , (b) A B , and (c) A B both in words and as subsets of S . 2. Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized below shock resistance high low scratch high 70 9 resistance low 16 5 Suppose that one of the 100 disks is randomly selected. (a) List the sample space, S , of this experiment. (b) Give the subset of S that corresponds to the event that the selected disk has low shock resistance. (c) Give the subset of S that corresponds to the event that the selected disk has low shock resistance or low scratch resistance. (d) What is the probability that the selected disk has low shock resistance? (e) What is the probability that the selected disk has low shock resistance or low scratch resistance? 3. Suppose that in State College 40% of the households subscribe to newspaper A, 30% to newspaper B, and 60% of the households subscribe to at least one of the two newspapers. Let A denote the event that a randomly chosen household subscribe to newspaper A, and let B denote the corresponding event for newspaper B. (a) Make a Venn Diagram showing events A and B and shade the region which has probability 0.4. 1 (b) Make a Venn Diagram showing events A and B and shade the region which has probability 0.3. (c) Make a Venn Diagram showing events A and B and shade the region which has probability 0.6. (d) Make a Venn Diagram showing events A and B , shade the event that a ran domly selected household subscribes to both newspapers, and find the proba bility of the shaded event. (e) Find the probability that a randomly selected household subscribes only to newspaper A (that is, subscribes to A but not to B)....
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This note was uploaded on 01/11/2012 for the course STAT 401 taught by Professor Akritas during the Fall '00 term at Penn State.
 Fall '00
 Akritas

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