Calculating Expected Value for Independent Selections | A and B | Catalog Items

[talolard]

Homework Statement

A catalog contains 10 itmes. Two people, A and B each select 3 items from the catalog independently. What is the expected value of the number of items A and B ordered.

My attempt:
Let A chose any 3 items. The probability that B
Chose 1 similar item is 3/10
Chose 2 of the same items = 3/10*2/9
Chose 3 of the same items = 3/10*2/9*1/8

And so the expected value is 1*(3/10) +2*(3/10*2/9) + 3*(3/10*2/9*1/8) = 11/24
But he awnsers page sais it is 0.9
I don't really know what I'm doing wrong
Guidance needed :)

 

[owlpride]

How did you compute your probabilities?

 

[talolard]

A chose any 3 items.
Then the chance that B chose one of them is 3/10. He has three chances to chose one of ten objects. The chance that B chose 2 of the same is 3/10*2/9 since he had 3 chances for the first one and two chances out of the nine remaining for the next one. etc

 

[owlpride]

The probability that the first item B chooses is one of A's items is 3/10. But what about the other two? With no restriction, they could be anything: one of A's or not one of A's, coincidental with the first item, etc.

 

[talolard]

I don't see why.
The chance that B took one item is 3/10. Then to chose another item he has two choices left out of 9 other items. So 2/9 and multiply by 3/10 since to get the seconed item he had to get the first item.

 

[owlpride]

Suppose you want to know the probability that B chooses exactly one of A's items. Then he has to choose one of the 3 items of A, and two of the remaining 7.

 

[talolard]

Ok. I got it. Thanks for the help, much apreciated.
Tal