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1. ## A probability problem

Hi all,
I would like to solve the problem bellow. To some it might seem to eassy. However i would appreciate some hints.

here is the statement:

"A new ornament has been released by a manufacturer. They made 1000 of the ornaments in total, but 350 were made from glass and the rest were made from clay. The ornaments are sold in a sealed box, so when buying the ornament it is not possible to tell whether you have a glass or a clay edition. Upon an impact, the glass ornaments have a 9/10 probability of breakin, and the clay ornaments have a 2/10 probability of breaking. To resell a broken ornament is worth nothing regardless of what is made of, a glass ornament is worth £100 and the clay ornament is worth £10. You just bought an ornament, but than dropped it before you could see what is made of. What is the expected value of your ornament now?"

2. ## Re: A probability problem

Now, before gettin further i would like to post what i have understood...
once again please correct me where i m wrong
thanks
____________

i think that we should find the probabiliti of the ornament of being broken.
it means that a 'logical' approach could sound like this:

Pb<=>(P_glass and P_glass_b) or (P_clay and P_clay_b)
where
Pb is the probability of the ornament to be broken
P_glass - probability that the ornament to be made out of glass
P_glass_b - probability of the glass ornament to be broken
and so on

=>
Pb = (.35*.9)+(.65*.2)=.45

so the probability of the ornament to be broken is about 45%.
what i need to know is, how do you translate that into the expected value?

3. ## Re: A probability problem

You should know that there are 4 scenarios, and each scenario will have its corresponding reselling value. Then you can calculate the probability of each scenario happening, and apply the formula of expected value to calculate it.

4. ## Re: A probability problem

what would be the expected value formula?

5. ## Re: A probability problem

So have you learn the formula calculating the expected value of a discrete random variable (the reselling value)?

6. ## Re: A probability problem

no, i have no ideea how to calculate that or where to get it from

7. ## Re: A probability problem

http://en.wikipedia.org/wiki/Expecte...2C_finite_case

If you really do not know anything about expected value, I suggest you to take a look with those introductory probability materials first before you move on. This is the basic background knowledge required for this question and for most of the probability questions, we assume you already familiar with this. So there will be a problem if you miss this important part in your study process.

8. ## The Following User Says Thank You to BGM For This Useful Post:

marius15 (04-26-2015)

9. ## Re: A probability problem

thanks
it was really usefull

so the expected value is:
E = value_of_unbroken_clay_orn*(Probability_that_unbroken_clay_orn_occur)+value_of_broken_clay_orn*(Probability_that_unbroken_clay_orn_occur)+
+value_of_unbroken_glass_orn*(Probability_that_unbroken_glass_orn_occur)+value_of_broken_glass_orn*(Probability_that_unbroken_glass_orn_occur)

=>

E = 10*(.65*.8) + 0*(.65*.2) + 100*(.35*.1) + 0*(.35*.9) = 8.7

thanks again for the hints

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