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Statistics / Probability and Statistical Inference 9 / Chapter 1.1 / Problem 1.1-15

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

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Let S = A1 A2 Am, where events A1, A2, ... , Am are mutually exclusive and exhaustive

Chapter 1, Problem 1.1-15

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QUESTION:

Let S = A1 A2 Am, where events A1, A2, ... , Am are mutually exclusive and exhaustive. (a) If P(A1) = P(A2) = = P(Am), show that P(Ai) = 1/m, i = 1, 2, ... , m. (b) If A = A1 A2 Ah, where h < m, and (a) holds, prove that P(A) = h/m.

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QUESTION:

Let S = A1 A2 Am, where events A1, A2, ... , Am are mutually exclusive and exhaustive. (a) If P(A1) = P(A2) = = P(Am), show that P(Ai) = 1/m, i = 1, 2, ... , m. (b) If A = A1 A2 Ah, where h < m, and (a) holds, prove that P(A) = h/m.

ANSWER:

Step 1 of 4

Give that are mutually exclusive events, that is, all the events impossible to occur together,

And also the events are exhaustive that is there union forms the sample space

Probability of is given by

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