Lstadt wrote:
Five A-list actresses are vying for the three leading roles in the new film, "Catfight in
Denmark." The actresses are Julia Robards, Meryl Strep, Sally Fieldstone, lauren
Bake-all, and Hallie Strawberry. Assuming that no actress has any advantage in getting
any role, what is the probability that Julia and Hallie will star in the film together?
Why isn't this approach right?
This is how I am doing it and I end up getting 2/5 which is not right.
I am doing the following:
Julia first (1/5) and Hallie second (1/4) = (1/5 * 1/4) OR
Hallie first (1/5) and Julia second (1/4) = (1/5 * 1/4) OR
Julia first (1/5) and Hallie third (1/3)=(1/5 * 1/3) OR
Hallie first (1/5) and Juila third (1/3)= (1/5 * 1/3) OR
Julia second (1/4) and Hallie third (1/3) = (1/4 * 1/3) OR
Hallie second (1/4) and Julia third (1/3) = (1/4 * 1/3)
I add them all up which totals to 2/5
Anything wrong here?
Here is your problem:
Julia first (1/5) and Hallie second (1/4) and anyone else third = (1/5 * 1/4 * 1) OR
Hallie first (1/5) and Julia second (1/4) and anyone else third = (1/5 * 1/4 * 1) OR
Julia first (1/5), someone other than Hallie second and Hallie third (1/3)=(1/5 * 3/4 * 1/3) OR
Hallie first (1/5), someone other than Julia second, and Juila third (1/3)= (1/5 * 3/4 * 1/3) OR
Someone other than Hallie and Julia first, Julia second (1/4) and Hallie third (1/3) = (3/5 * 1/4 * 1/3) OR
Someone other than Hallie and Julia first, Hallie second (1/4) and Julia third (1/3) = (3/5 * 1/4 * 1/3)
When you add them up, you get 6/20 = 3/10
Another way to do it:
Pick Hallie and Julia. Now you can pick the third actress in 3 ways so total number of ways of picking 3 actresses (including Hallie and Julia) = 3
Total number of ways of picking any 3 actresses out of 5 = 5*4*3/3! = 10
Probability that both Hallie and Julia will be picked = 3/10