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February 14th, 2016, 08:54 PM   #1
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One container holds the letters D A D and a second container holds the letters A D D. One letter is chosen randomly from the first container and added to the second container. Then a letter will be chosen from the second container.

a) What is the probability that the second letter chosen is D if the first letter was A? If the first letter was D?

b) What is the probability that the second letter chosen is A if the first letter was A? If the first letter was D?

My attempt:

a) If the first letter chosen is A, then the second container now contains A A D D. Therefore P(second letter chosen is D) = 2/4 = 1/2
If the first letter chosen is D, then the second container now contains A D D D. Therefore P(second letter chosen is D) = 3/4

b) If the first letter chosen is A, the second container now has A A D D. Therefore, P(the second letter chosen is A) = 2/4 = 1/2
If the first letter chosen is D, the second container now has A D D D. Therefore, the P(second letter is A) = 1/4

Am I correct? Is there a different/better/easier way to solve this? Thanks.
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February 15th, 2016, 01:12 AM   #2
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You have given two different probabilities for each part. A single answer needs to be given for each part.
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February 15th, 2016, 01:16 AM   #3
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Quote:
Originally Posted by Prakhar View Post
You have given two different probabilities for each part. A single answer needs to be given for each part.
I don't understand. Can you show me the way. Thanks
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February 15th, 2016, 01:21 AM   #4
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Both containers contain the letters A, D and D. Does their order have any relevance?

This problem can be neatly solved with a table.
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February 15th, 2016, 01:22 AM   #5
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You say that if the letter chosen is A or if the letter chosen is B. But, while choosing the letter, we don't know what has been chosen (because if we know, we don't need the concept of probability). I think that after finding the two possible outcomes, you should find their mean and write it as the final answer (in each part).
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February 15th, 2016, 01:32 AM   #6
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For the first container, you could say that:

A_1, D_1 and D_2 exist.

For the second container, you could say that:

A_2, D_3 and D_4 exist.

------------------

If D_1 is selected from the first container and placed in the second container, in the second container:

A_2, D_1, D_3 and D_4 would exist.

If D_2 is selected from the first container and placed in the second container, in the second container:

A_2, D_2, D_3, and D_4 would exist.

If A_1 is selected from the first container and placed in the second container, in the second container:

A_1, A_2, D_3 and D_4 would exist.

-----------------------

These are all possible scenarios. You can think of the A's and D's as unique objects.

----------------------

Using the logic above you can deduce that:

a.1) P(E_1)=1/2
a.2) P(E_2)=3/4

b.1) P(E_3)=1/2
b.2) P(E_4)=1/4

Last edited by perfect_world; February 15th, 2016 at 01:38 AM.
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February 15th, 2016, 01:38 AM   #7
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Quote:
Originally Posted by perfect_world View Post
For the first container, you could say that:

A_1, D_1 and D_2 exist.

For the second container, you could say that:

A_2, D_3 and D_4 exist.

------------------

If D_1 is selected from the first container and placed in the second container, in the second container:

A_2, D_1, D_3 and D_4 would exist.

If D_2 is selected from the first container and placed in the second container, in the second container:

A_2, D_2, D_3, and D_4 would exist.

If A_1 is selected from the first container and placed in the second container, in the second container:

A_1, A_2, D_3 and D_4 would exist.

-----------------------

These are all possible scenarios. You can think of the D's as unique objects.
I don't think that we need the concept of A1, A2 or D1, D2 because only one letter is chosen from the first container. It is either A or D. Whether it is the first A or second or whether it is the first D or second doesn't matter.
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February 15th, 2016, 01:41 AM   #8
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I'm just pedantic. @Shunya wanted a solid explanation as to why his results were correct. I gave him a detailed and robust response. I don't have to water anything down.
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