# 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

Appeared in Year: 2012

### 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

## Question number: 2

» Probability » Bayes' Theorem

Appeared in Year: 2014

### 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

Similarly, Probability of selecting a