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Statistics / Probability and Statistical Inference 9 / Chapter 1.1 / Problem 1.1-5

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

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Consider the trial on which a 3 is first observed in successive rolls of a six-sided

Chapter 1, Problem 1.1-5

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QUESTION:

Consider the trial on which a 3 is first observed in successive rolls of a six-sided die. Let A be the event that 3 is observed on the first trial. Let B be the event that at least two trials are required to observe a 3. Assuming that each side has probability 1/6, find (a) P(A), (b) P(B), and (c) P(A B).

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QUESTION:

Consider the trial on which a 3 is first observed in successive rolls of a six-sided die. Let A be the event that 3 is observed on the first trial. Let B be the event that at least two trials are required to observe a 3. Assuming that each side has probability 1/6, find (a) P(A), (b) P(B), and (c) P(A B).

ANSWER:

Step 1 of 4

Let us first recall some basic rules.

Complement rule:

Addition rule for disjoint or mutually exclusive events:

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