Help please with probability problem?

Question

A man wants to determine whether or not to invest $1000 in a friend's speculative venture. He will do so if he thinks he can get his money back in one year. He believes the probabilities of the various outcomes at the end of one year are as follows:
Results Probability
$2000----------0.3
$1500----------0.1
$1000----------0.2
$500------------0.3
$0---------------0.1
What would be his expected outcome if he invests the $1000?
Please explain the answer if you can figure it out.

Answer 1

30% of the time he will get $2,000.
0.3 x 2,000 = $600
10% of the time he will get $1,500
0.1 x 1,500 = $150
20% of the time he will get $1,000
0.2 x 1,000 = $200
30% of the time he will get $500
0.3 x 500 = $150
10% of the time he will get nothing
0.1 x 0 = $0

Adding it up he is expect to get $1,100. He should invest.

If you have a series of outcomes (a, b, c, d, ...) with probabilities (p1, p2, p3, p4, ...) the expect outcome is essentially a weighted average of the outcomes:

(p1 x a) + (p2 x b) + (p3 x c) + (p4 x d) + ....

As shown above, he should expect a return of $1,100 on his investment of $1,000. Certainly not a guarantee, but if he is a confident invester and can afford to lose half or all of his original investment, it would seem advantageous.

Answer 2

Just multiply each outcome by the probability it will occur, and then sum these products over all the outcomes.
$2000(.3) + $1500(.1) + $1000(.2) + $500(.3) + $0(.1) =
$600 + $150 + $200 + $150 + $0 = $1100

Answer 3

Hey,

i'm not sure about this, but i think it's:

(0.3 x 2000) + (0.1 x 1500) + (0.2 x 1000) + (0.3 x 500) + (0.1 x 0) = 1100 > 1000 So he should invest.