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# The first basket contains 4 blue and 5 red marbles; the second basket

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Math Expert
Joined: 02 Sep 2009
Posts: 57155

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28 Jan 2018, 21:26
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Difficulty:

25% (medium)

Question Stats:

74% (01:58) correct 26% (02:15) wrong based on 80 sessions

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The first basket contains 4 blue and 5 red marbles; the second basket contains 3 blue and 4 red marbles. One marble is randomly extracted from the first basket and put into the second. After that, a marble is extracted from the second basket. What is the probability that this marble is blue?

A. 1/3
B. 15/36
C. 31/72
D. 4/9
E. 11/18

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28 Jan 2018, 21:53
2
Has to be C.

There are two cases.

Case 1:
Selection of blue from first bag followed by the selection of blue from the second bag.

Selection of blue from first bag = 4/9.
Now the total blue balls in second bag becomes 4 with total balls as 8.
Hence selection of blue from second bag = 4/8.
Total probability = 4/9*4/8 =16/72

Case 2:
Selection of red from first bag followed by the selection of blue from the second bag.

Selection of red from first bag = 5/9.
Now the total red balls in second bag becomes 5 with total balls as 8.
Hence selection of blue from second bag = 3/8.
Total probability = 5/9*3/8 =15/72

Total probability = 16/72 + 15/72 = 31/72
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28 Jan 2018, 23:23
Bunuel wrote:
The first basket contains 4 blue and 5 red marbles; the second basket contains 3 blue and 4 red marbles. One marble is randomly extracted from the first basket and put into the second. After that, a marble is extracted from the second basket. What is the probability that this marble is blue?

A. 1/3
B. 15/36
C. 31/72
D. 4/9
E. 11/18

We have 2 events and based on their sequences, following combinations are possible :
1. Take blue from basket 1 and place it in basket 2. In this case, probability of picking blue is :
4/9 * 4/8 =16/72
2. Take red from basket 1 and place it in basket 2. In this case, probability of picking blue is :
5/9*3/8=15/72

Since either of two events are possible, we have
16/72 + 15/72 = 31/72 as answer.
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02 Feb 2019, 00:13
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Re: The first basket contains 4 blue and 5 red marbles; the second basket   [#permalink] 02 Feb 2019, 00:13
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