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Statistics / Probability and Statistical Inference 9 / Chapter 1.5 / Problem 1.5-1

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

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Bowl B1 contains two white chips, bowl B2 contains two red chips, bowl B3 contains two

Chapter 1, Problem 1.5-1

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QUESTION:

Bowl \(B_1\) contains two white chips, bowl \(B_2\) contains two red chips, bowl \(B_3\) contains two white and two red chips, and bowl \(B_3\) contains three white chips and one red chip. The probabilities of selecting bowl \(B_1, B_2, B_3\), or \(B_4\) are 1/2, 1/4, 1/8, and 1/8, respectively. A bowl is selected using these probabilities and a chip is then drawn at random. Find

(a) P(W), the probability of drawing a white chip.

(b) \(P(B_1 | W)\), the conditional probability that bowl \(B_1\) had been selected, given that a white chip was drawn.

Questions & Answers

QUESTION:

Bowl \(B_1\) contains two white chips, bowl \(B_2\) contains two red chips, bowl \(B_3\) contains two white and two red chips, and bowl \(B_3\) contains three white chips and one red chip. The probabilities of selecting bowl \(B_1, B_2, B_3\), or \(B_4\) are 1/2, 1/4, 1/8, and 1/8, respectively. A bowl is selected using these probabilities and a chip is then drawn at random. Find

(a) P(W), the probability of drawing a white chip.

(b) \(P(B_1 | W)\), the conditional probability that bowl \(B_1\) had been selected, given that a white chip was drawn.

ANSWER:

Step 1 of 4

Given,

Chips:	White	Red
	2
		2
	2	2
	3	1

Let’s determine the following:

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