A painter intends to mixed two jars of paint to create a new color. He

Question

A painter intends to mixed two jars of paint to create a new color. He chooses one paint jar randomly from a display containing 2 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. If he plans on mixing the two chosen jars together, what is the probability that when mixed together, the result will be purple paint? (The color purple is created with 1 part red and 1 part blue.)

A. 1/5
B. 1/2
C. 2/3
D. 4/5
E. 6/5

A. 1/5
B. 1/2
C. 2/3
D. 4/5
E. 6/5

Archit3110 · Answer

purple = 1 red + 1 blue
P = 2/4 * 2/5 + 2/4*3/5 
=> 1/5+3/10 ; 1/2
IMO B

kornn · Answer

Dear  GMATGuruNY ,

For example, if the question were:

1st jar containing 100 red and 2 blue samples
2nd jar 3 red and 50 blue samples

The answer would be:
1st Red 2nd Blue --> 1st Red (1st pick) = 100/102 whereas 2nd Blue (2nd pick) = 50/53

1st pick isn't necessarily equal to 2nd pick.

I'm very confused here.

GMATGuruNY · Answer

Yes, the highlighted rule applies only when every pick is from the same source.

kornn · Answer

Dear GMATGuruNY , Then why is this question considered choosing from the same source? He chooses one paint jar randomly from a display containing 2 red and 2 blue samples, and a second jar is chosen at random from a different display containing 3 red and 2 blue samples. I'm completely lost here. Please help sir

IanStewart · Answer

I don't understand what that solution is saying either. There is a simple way to look at this problem to get the answer 1/2, but the above solution appears to be backwards. The point is, it doesn't matter which colour the painter chooses from the 3-red, 2-blue shelf (the numbers here could be anything at all). Either way, when he picks from the 2-red, 2-blue shelf, he will have a 1/2 probability of picking the "right" colour to make purple paint. So the answer is 1/2.

This method relies completely on the fact that we have an equal number of red and blue paint cans on one of the shelves. You can't adapt this method to other situations.

GMATGuruNY · Answer

In retrospect, I would not apply the highlighted rule to this problem.
To avoid confusion, I've edited the earlier post.
The edited post now offers a more straightforward solution.

A painter intends to mixed two jars of paint to create a new color. He

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A painter intends to mixed two jars of paint to create a new color. He

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