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There are two bags A and B. Bag A contains 2 white and 3 black balls.

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Bunuel
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There are two bags A and B. Bag A contains 2 white and 3 black balls. [#permalink] New post   28 Jan 2021, 05:40
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69% (01:25) correct 31% (01:54) wrong based on 67 sessions
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There are two bags A and B. Bag A contains 2 white and 3 black balls. Bag B contains 3 white and 4 black balls. A bag is chosen at random. What is the probability that the ball drawn is white?

A. 29/70
B. 5/12
C. 1/2
D. 31/70
E. 7/12

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A
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Re: There are two bags A and B. Bag A contains 2 white and 3 black balls. [#permalink] New post   28 Jan 2021, 06:18
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Bunuel wrote:
There are two bags A and B. Bag A contains 2 white and 3 black balls. Bag B contains 3 white and 4 black balls. A bag is chosen at random. What is the probability that the ball drawn is white?

A. 29/70
B. 5/12
C. 1/2
D. 31/70
E. 7/12


Bag A contains 2 white and 3 black balls
Bag B contains 3 white and 4 black balls

Case 1: Bag chosen is Bag A



Probability of Bag A to be chosen \(= \frac{1}{2}\)
Probability of White ball being chosen from Bag A \(= \frac{2}{5}\)

i.e. Probabilty that Case 1 happens \(= (\frac{1}{2})*(\frac{2}{5}) = \frac{1}{5}\)

Case 2: Bag chosen is Bag B



Probability of Bag B to be chosen \(= \frac{1}{2}\)
Probability of White ball being chosen from Bag B \(= \frac{3}{7}\)

i.e. Probabilty that Case 2 happens \(= (\frac{1}{2})*(\frac{3}{7}) = \frac{3}{14}\)

Required Probability = Case 1 or Case 2 \(= \frac{1}{5} + \frac{3}{14} = \frac{29}{70}\)



Answer: Option A
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Re: There are two bags A and B. Bag A contains 2 white and 3 black balls. [#permalink] New post   03 Feb 2021, 23:52
IMO A
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Re: There are two bags A and B. Bag A contains 2 white and 3 black balls. [#permalink] New post   08 Feb 2021, 12:22
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Bunuel wrote:
There are two bags A and B. Bag A contains 2 white and 3 black balls. Bag B contains 3 white and 4 black balls. A bag is chosen at random. What is the probability that the ball drawn is white?

A. 29/70
B. 5/12
C. 1/2
D. 31/70
E. 7/12

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Solution:

P(white ball) = P(white ball from bag A) * P(bag A) + P(white ball from bag B) * P(bag B)

= 2/5 * 1/2 + 3/7 * 1/2

= 1/5 + 3/14 = 14/70 + 15/70 = 29/70

Answer: A
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Re: There are two bags A and B. Bag A contains 2 white and 3 black balls. [#permalink]
08 Feb 2021, 12:22
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