Person in company has to present proposition for purchase of one of three computers with same prices. Purchase of each computer working without failure for a year provides economical gain. Although during this year an failure of software , hardware or both might occur. It is known that failure during a year might be only one. Fixing the failure will be some economical loss.
a) Which computer should be bought to maximize economical gains during the year
b) The probability of a beneficial event occurring which will have an effect of at least $22$
c) the probability of an unbenneficial event which will have an economical effect of not more than $15$
My proposed solution:
a)
I think for a) I need to calculate expected value of each computer for cases: without failure,hardware failure,software failure, soft & hardware failure(?) so
For computer 1:
$18*0,8+15*0,06+17*0,1+14*0,04 = 17,56 $
And calculate the same thing for computer 2 and 3 and the one with the highest expected value will be the winner(?). Is that the right approach?
b) and c)
Regarding b) I think I have somehow sum number of cases where I will get effect higher than 22 and then divide it by all possible cases(?) same with c) but sum number of all cases where economical benefits will be not more than 15. Although I feel that I have to include somewhere probability of each case(economical gain higher than 22 or less than 15).
Is my thinking right? Sorry for my not perfect english.