Word Translation Chapter 5 Question 11

[ayush.sharma]

I did this in this manner and cant see why the book has a different answer :
Number of spots : 3
Number of actresses : 5
Spot 1 Spot 2 Spot 3
J H X
X J H
H X J
J X H
X H J
H J X

Prob of (J and H)=
(1/5)*(1/4)+
(1/4)*(1/3)+
(1/5)*(1/3)+
(1/5)*(1/3)+
(1/4)*(1/3)+
(1/5)*(1/4).=== 2/5.

I cant see what is wrong with this approach.
The book assumes that the case where julia is cast first = 1/5 and then the fact that halle is cast second = 1/4 is consistent throughout the table and hence multiples 1/5 *1/4 *6.
I disagree with it -- Maybe I am making a silly mistake somewhere or I am totally wrong on this :)
Please help me see where I have gone wrong.
Thanks.

[tim]

i'm going with "totally wrong". :) your setup and calculations are incomprehensible, and unfortunately i can't tell at all what you are trying to do. here's what i'd like you to do: rewrite your solution with a full explanation of each step. tell us why you set each thing up the way you did and what each calculation represents. if you can do this, we'll be able to figure out where things went wrong and how to help you..

[ayush.sharma]

Tim,
The line which reads
SPOT 1....SPOT3 are the columns/slots that represent the vacancies for the roles for the actresses.
And J and H stand for the actresses names- Julia and Hollie if i am not wrong.
SPOT 1....SPOT2....SPOT3
J.............H...........X

This means that Julia was chosen first for spot 1 and then holly was chosen for spot 2 and we dont care who was chosen for the third spot.

So Prob of J and H for the first scenario will be : (1/5)*(1/4)...
Hope this helps.

[ayush.sharma]

i'm going with "totally wrong". :) your setup and calculations are incomprehensible, and unfortunately i can't tell at all what you are trying to do. here's what i'd like you to do: rewrite your solution with a full explanation of each step. tell us why you set each thing up the way you did and what each calculation represents. if you can do this, we'll be able to figure out where things went wrong and how to help you..

Also Tim - with much respect - if my setup and calculations are incomprehensible then how can you reach the conclusion that my approach is totally wrong...... since you said you couldn't tell what I had done...."

[tim]

I think I see what you're doing now. The problem is that each of the terms you added include probabilities for J and H, but you have omitted the calculation for X. Add those in and you'll see that you are now adding 6 terms, each of which equals 1/20. In other words, your calculation should look like this:

(1/5)*(1/4)*(3/3)+
(3/5)*(1/4)*(1/3)+
(1/5)*(3/4)*(1/3)+
(1/5)*(3/4)*(1/3)+
(3/5)*(1/4)*(1/3)+
(1/5)*(1/4)*(3/3)= 3/10

In your initial post you offered the choice between "silly mistake" and "totally wrong"; I guessed "totally wrong" because I didn't have enough information to conclude that it was a "silly mistake". Now that you've explained your reasoning it does look more like this was just a "silly mistake". Turns out you were actually pretty close in fact. Thanks for clarifying; I hope this explanation helps..