# Math Help - investment problem

1. ## investment problem

you have two dependent investments
investment A 20a .7
investment B 20b .3
a=how much you invest in A
b=how much you invest in B
both investments pay 20 times your money
investment A will succed .7 and if it fails investment B succeds
so,
Investment A .7
Investment B .3

If you did this experiment an infinite number of times your expected value is
E=.7(20a)+.3(20b)
E= 14a+6b
so,
All your money should go with A even if A only succeded 51% of the time.

but say I gave you 100$and I said this experiment will only be run one time. it would not be very smart to invest it all in A for there is a .3 chance you will go broke. (you don't want that to happen) So how would you invest your money? and why? what about if i ran the experiment 2 times or 3 or 4 thanks 2. ## Re: investment problem Your payoffs for the investment are huge so you can guarantee a no loss investment if you put$95 In A and 5 in B and worst case scenario is that A fails and therefore B succeeds so you get your $100 back. If you were risk adverse you might just take the guaranteed profit by putting more than$5 in B. For example, if you split is 90-10 you can't possibly lose under your assumptions.

To maximize profits you would still put it all in A but your point is that you have no minimized your losses. You can guarantee to walk away with 1000 by splitting 50-50 into A and B because no matter what happens one investment pays off 20*50 and thus you've turned your 100 into 1000.

(I am assuming that you meant if A fails then B succeeds and if B fails then A succeeds)

3. ## Re: investment problem

so assuming the experiment is run once 50/50 is best.
so it does not matter the probabilities of success and failer, all that matters is that if one fails the other succeeds. so even if the prob are .95 for A and .05 for B 50/50 is your best bet since it minimizes your loss.
so 50/50 would still be best no matter what the prob are right?