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A bag contains 2 white and 3 red balls, and a bag B contains 4 white

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A bag contains 2 white and 3 red balls, and a bag B contains 4 white  [#permalink]

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New post 31 Jan 2019, 07:25
2
5
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

42% (02:32) correct 58% (01:54) wrong based on 24 sessions

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A bag contains 2 white and 3 red balls, and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and it is found to be red.
Find the probability that it was drawn from the bag B
A) \(\frac{5}{52}\)
B) \(\frac{15}{52}\)
C) \(\frac{25}{52}\)
D) \(\frac{35}{52}\)
E) \(\frac{45}{52}\)

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Re: A bag contains 2 white and 3 red balls, and a bag B contains 4 white  [#permalink]

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New post 31 Jan 2019, 08:07
Probability of extracting a Red ball

1/2*(3/5)+1/2*(5/9) = 26/45

Probability of estracting a Rell ball from Bag B:

1/2*5/9 =5/18


(5/18)/(26/45) = 25/52 Answer C
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Re: A bag contains 2 white and 3 red balls, and a bag B contains 4 white  [#permalink]

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New post 04 Feb 2019, 19:15
2
4d wrote:
A bag contains 2 white and 3 red balls, and a bag B contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and it is found to be red.
Find the probability that it was drawn from the bag B
A) \(\frac{5}{52}\)
B) \(\frac{15}{52}\)
C) \(\frac{25}{52}\)
D) \(\frac{35}{52}\)
E) \(\frac{45}{52}\)


This is a conditional probability problem since it is asking: given that the ball is red, what is the probability it is from bag B?

We can use the following formula:

P(bag B, given it’s a red ball) = P(a red ball from bag B)/P(a red ball)

Assuming there is an equal chance of picking either bag, we have:

P(a red ball from bag B) = 5/9 x 1/2 = 5/18

P(a red ball) = P(a red ball from bag B) + P(a red ball from bag A) = 5/9 x 1/2 + 3/5 x 1/2 = 5/18 + 3/10

Therefore, the probability in question is:

(5/18)/(5/18 + 3/10)

Multiply the numerator and the denominator by 90, we have:

25/(25 + 27) = 25/52

Alternate Solution:

We notice that the probability of picking a red ball from bag A is 3/5 and the probability of picking a red ball from bag B is 5/9. If the two probabilities were equal, then the probability that the ball was drawn from bag A would have been equal to the probability that the ball was drawn from bag B. However, since 3/5 = 27/45 > 5/9 = 25/45, there is a greater probability that the ball was drawn from bag A. Thus, the probability that the ball was drawn from bag B should be less than 1/2. Furthermore, since the two probabilities 27/45 and 25/45 are very close to each other, probability that the ball was drawn from bag B should be very close to (but less than) 1/2. Going over the answer choices, 25/52 is the choice that fits best with this.

Answer: C
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Re: A bag contains 2 white and 3 red balls, and a bag B contains 4 white  [#permalink]

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New post 07 Feb 2019, 08:32
Bunuel Can you please clarify regarding conditional probability applied here ?
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Re: A bag contains 2 white and 3 red balls, and a bag B contains 4 white   [#permalink] 07 Feb 2019, 08:32
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A bag contains 2 white and 3 red balls, and a bag B contains 4 white

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