Posted by **Amelie** on Saturday, February 23, 2008 at 7:14pm.

two construction contracts are to be randomly assigned to one or more of 3 firms- I,II,III. A firm may receive more than one contract. if each contract has a potential profit of 90,000 dollars. find the expected potential profit for firm I. then find the expected potential profit for firms I and II together.

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Can i start by using the expected value formula?

- Intro to Probability -
**drwls**, Saturday, February 23, 2008 at 7:38pm
Yes, this looks like an expected value problem. The probability of one or the other getting a contract both times (2/3)^2 = 4/9. The probability of I or II getting one only is 2*1/3*2/3= 4/9. The probability of missing out both times is 1/9.

E.V. = (4/9)*180,000 + (4/9)*90,000) = ?

- Intro to Probability -
**amelie**, Saturday, February 23, 2008 at 7:41pm
thank you drwls for your help I greatly appreciate it.

- Intro to Probability -
**Damon**, Saturday, February 23, 2008 at 7:47pm
For firm 1

Probability of getting contract a only = probability of getting a - probability of getting both = 1/3 - 1/9 = 2/9

Probability of getting contract b only = 2/9

Probability of getting a and b both = 1/9

so

E($) = (4/9)90 k + (1/9) 180 k

= 40 + 20

= $60 K

- Intro to Probability -
**drwls**, Saturday, February 23, 2008 at 7:53pm
I get 120K. With a total of 180K awarded, it seems to make sense that two of the three firms would, on the average, get 2/3 of it

- Intro to Probability -
**Damon**, Saturday, February 23, 2008 at 8:49pm
for 2 firms together:

There are still 9 possible configurations

probability of 1 getting A and 2 getting B = probability of 1 getting B and 2 getting A = 1/9

so (2/9) * 180 k = 40k so far

Then 1 gets 0, 2 gets A 1/9

1 gets 0, 2 gets B 1/9

1 gets A, 2 gets 0 1/9

1 gets B, 2 gets 0 1/9

so 4/9 * 90k = 40k

Then 1 gets AB 1/9

2 gets AB 1/9

so again

(2/9)*180 k = 40 k

so in the end

3 * 40 k = 120 k

Which is just what drwls said, but done in a much more difficult if simple way.

- Intro to Probability -
**Damon**, Saturday, February 23, 2008 at 8:50pm
drwls

I did the one firm problem first.

- Intro to Probability -
**Damon**, Saturday, February 23, 2008 at 8:52pm
I think you missed the first of 2 parts of the question.

- Intro to Probability -
**amelie**, Saturday, February 23, 2008 at 9:48pm
thanks damon

- Intro to Probability -
**drwls**, Sunday, February 24, 2008 at 2:21am
Yes, I see that now. I just did the two firms together case. I should not skim through questions

- Intro to Probability -
**Anonymous**, Sunday, March 31, 2013 at 1:31pm
1/9

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