MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Educational Module: Probability Applications --- **Scenario**: Paul applies to sell souvenirs at a sporting event. He may be assigned to any of sections A through E, or he may be rejected. The table below shows the probabilities of his being assigned to a particular section or being rejected. | Section | Probability | |------------|-------------| | A | 0.1 | | B | 0.2 | | C | 0.2 | | D | 0.2 | | E | 0.1 | | Rejected | 0.2 | --- **Questions and Solutions**: **a)** What is the probability that Paul is assigned to section A? *The probability that Paul is assigned to section A is* \( \boxed{0.1} \). --- **b)** What equation can be used to find the probability that Paul is not assigned to section A? *The probability that Paul is not assigned to section A can be found using the equation:* \[ P(\text{not assigned to } A) = 1 - P(A) \] *Substitute the given probability into the formula:* \[ P(\text{not assigned to } A) = 1 - 0.1 = \boxed{0.9} \] --- **c)** What is the probability that Paul’s application is not rejected? *The probability that Paul’s application is not rejected can be found by summing the probabilities of him being assigned to sections A, B, C, D, or E. This can be calculated by subtracting the rejection probability from 1:* \[ P(\text{not rejected}) = 1 - P(\text{rejected}) \] *Substitute the given probability into the formula:* \[ P(\text{not rejected}) = 1 - 0.2 = \boxed{0.8} \] --- **d)** What is the probability that Paul is assigned to sections A, B, or C? *The probability that Paul is assigned to sections A, B, or C can be found by summing the probabilities of these sections:* \[ P(A \cup B \cup C) = P(A) + P(B) + P(C) \] *Substitute the given probabilities into the formula:* \[ P(A \cup B \cup C) = 0.1 +
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Transcribed Image Text:### Educational Module: Probability Applications --- **Scenario**: Paul applies to sell souvenirs at a sporting event. He may be assigned to any of sections A through E, or he may be rejected. The table below shows the probabilities of his being assigned to a particular section or being rejected. | Section | Probability | |------------|-------------| | A | 0.1 | | B | 0.2 | | C | 0.2 | | D | 0.2 | | E | 0.1 | | Rejected | 0.2 | --- **Questions and Solutions**: **a)** What is the probability that Paul is assigned to section A? *The probability that Paul is assigned to section A is* \( \boxed{0.1} \). --- **b)** What equation can be used to find the probability that Paul is not assigned to section A? *The probability that Paul is not assigned to section A can be found using the equation:* \[ P(\text{not assigned to } A) = 1 - P(A) \] *Substitute the given probability into the formula:* \[ P(\text{not assigned to } A) = 1 - 0.1 = \boxed{0.9} \] --- **c)** What is the probability that Paul’s application is not rejected? *The probability that Paul’s application is not rejected can be found by summing the probabilities of him being assigned to sections A, B, C, D, or E. This can be calculated by subtracting the rejection probability from 1:* \[ P(\text{not rejected}) = 1 - P(\text{rejected}) \] *Substitute the given probability into the formula:* \[ P(\text{not rejected}) = 1 - 0.2 = \boxed{0.8} \] --- **d)** What is the probability that Paul is assigned to sections A, B, or C? *The probability that Paul is assigned to sections A, B, or C can be found by summing the probabilities of these sections:* \[ P(A \cup B \cup C) = P(A) + P(B) + P(C) \] *Substitute the given probabilities into the formula:* \[ P(A \cup B \cup C) = 0.1 +
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