Probability-Bayes' Theorem (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 1 - 2 of 2

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Question number: 1

» Probability » Bayes' Theorem

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Appeared in Year: 2012

Essay Question▾

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The ith box contains 2i white balls and 6 - 2i black balls, i = 1 (1) 3. A fair die is cast once. 3 balls are taken at random from box 1, box 2 or box 3 according as the die shows up face 1, any of 2 and 3, or any of 4,5 and 6, respectively. Let X denotes the number of white balls drawn. Find E (X).

Explanation

E 1 = Box 1 2 white and 4 black when the fair dice value is x 1 =1

E 2 =Box 2 4 white and 2 black when the fair dice value is x 2 = (2,3)

E 3 =Box 3 6 white when the fair dice value is x 3 = (4,5, 6)

X denotes the number of white balls out of random

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Question number: 2

» Probability » Bayes' Theorem

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Appeared in Year: 2014

Essay Question▾

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There are three identical bags U 1, U 2 and U 3. U 1 contains 3 red and 4 black balls; U 2 contains 4 red and 5 black balls; U 3 contains 4 red and 4 black balls. One bag is chosen at random; a ball is drawn at random from the chosen bag and it is found to be red. Find the probability that the first bag is chosen.

Explanation

Given that there are three identical bags U 1, U 2 and U 3. Then probabilities of selecting a bag are,

Let X be the event of selecting a red ball

Probability of selecting a red ball in U 1 is

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