Word Translations - Probability Problem Set #11 Pg. 93

11. Five A-list actresses are vying for the three leading roles in the new film, "Catfight in Denmark." The actresses are Julia Robards, Merly Strep, Sally Fieldstone, Lauren Bake-all, and Hallie Strawberry. Assuming that no actresses has any advantage in getting any role, what is the probability that Julia and Hallie will star in the film together?

I was trying to use a 1-X approach to this problem and was coming up short. Can someone please explain why?

I added:

1) The chance neither will be in the film: (3/5)(2/4)(1/3) = 1/10
2) The chance of one actress not being casted: 4/10
3) The chance the other actress will not be casted: 4/10

Therefore 1/10 + 4/10 + 4/10 = 9/10 probability a scenario will occur where the two actresses will not be in the film

Then according to 1-X logic, is it not a 1/10 probability they will be in the film together?

I do understand if we take one actress being cast and the other being cast and an actress outside the two we get:
(1/5)(1/4)(3/3 or 1) = 1/20
and we multiply this by 6 viable combinations to get 6/20 or 3/10

Why am I getting 1/10 for my 1-x approach. Am I setting up the negative outcome incorrectly?

To make the explanation easier on me, let H stand for the actress Hallie and J for the actress Julia.

Statement (2), as you have it, also includes the case where both H and J are not chosen which is case (1) and leads to an overlap. What statements (2) and (3) should be are
(2)The chance J will not be cast AND H will be cast.
(3)The chance H will not be cast AND J will be cast.

good explanation John; thanks..

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Tim Sanders
Manhattan GMAT Instructor

I have a question about this.

If you approach this problem as the chances of the 2 actresses being picked and the probabilities are:
1/5, 1/4, 1; then what about when that is not the order in which they are picked? For example: Julia is 1, Meryl is 2, Hallie is 3. Wouldnt the probabilities then be:
1/5, 1, 1/3?

This would result in a different answer. What am I missing here?

Did you only read what's typed above or did you read the explanation in the book? In the book, the part of the explanation that multiplies by 6 is the part that addresses the different possible orders in which they could be picked. That part of the explanation starts with "There are six event chains..." Go check it out if you haven't already!

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Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

still the explanation still not clear, isn't there a way to use the combination Formula?

did you read the explanation in the book?

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Tim Sanders
Manhattan GMAT Instructor