# 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▾

### Describe in Detail

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

… (57 more words) …

## Question number: 2

» Probability » Bayes' Theorem

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

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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