Question

An engineering consultant bids on jobs where he can make $10000 profit. If in a certain month, he has a 20% probability of getting a contract, 30% probability of getting 2 contracts, 40% probability of getting 3 contracts, and 10% probability of getting 4 contracts, what is the consultant’s expected profit for that month?

Answer 1

These events are are not independent. If he gets one contract, he cannot get two, etc.

If he gets one, then he has a .2 chance of getting a second one, then, if that occurs, he has a .4 chance of getting a third, ....

expected value=.2P+.2*.3* P+.2*.3*.4* P+.2*.3*.4*.1* P
= (.2+.06+.024+.0024)P
where P is 10,000
check my numbers

looks to be 10,000*.2864) check it.