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

In summary, the expected value of the number of items A and B ordered is 11/24. The probability that B chooses exactly one of A's items is 3/10 * 2/9 * 7/8 = 7/120. This means that out of the 10 items in the catalog, there is a 7/120 chance that A and B will each choose one of the same items. The remaining 113/120 chance is that they will choose items that are different from each other. This results in an expected value of 11/24, which is different from the answer given in the page, which is 0.9. Further clarification may be needed to determine the correct answer.
  • #1
talolard
125
0

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 :)
 
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  • #2
How did you compute your probabilities?
 
Last edited:
  • #3
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
 
  • #4
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.
 
  • #5
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.
 
  • #6
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.
 
  • #7
Ok. I got it. Thanks for the help, much apreciated.
Tal
 

What is expected value?

Expected value refers to the average outcome of a random event in a given situation. It is calculated by multiplying each possible outcome by its probability and then summing them together.

How do you calculate expected value?

To calculate expected value, you multiply the value of each possible outcome by its probability and then add them together. For example, if there is a 50% chance of winning $100 and a 50% chance of losing $50, the expected value would be (0.5 x $100) + (0.5 x -$50) = $25.

What does a positive expected value mean?

A positive expected value means that, on average, you can expect to gain money from a given situation. It indicates that the potential gain outweighs the potential loss.

Why is expected value important in decision making?

Expected value is important in decision making because it allows you to make informed choices based on the potential outcomes of a situation. By calculating the expected value, you can determine the probability and potential gain or loss associated with a decision.

How does expected value relate to risk?

Expected value is a measure of risk because it takes into account the probability of different outcomes. A higher expected value indicates a higher potential gain, but it also means there is a higher level of risk involved.

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