# Thread: Probability that profit will be $8000 or more... 1. ## Probability that profit will be$8000 or more...

Suppose you have $100,000 to invest in stocks. If you invest$1000 in any particular stock your profit will be $200,$100, $0 or -$100 (a loss), with probability 0.25 each. There are 100 different stocks you can choose from, and they all behave independently of each other. Consider the 2 cases: (1) Invest $100,000 in one stock. (2) Invest$1000 in each of 100 stocks.

a) For case (1) find the probability that your profit will be $8000 or more b) Do the same for case (2) So I'm thinking for a) if you invest all$100,000 in one stock it would raise the profits to $20,000,$10,000, $0, or -$10,000, but I don't know how you'd figure out it it'd be $8000 or more? Please help! 2. Originally Posted by bart203 Suppose you have$100,000 to invest in stocks. If you invest $1000 in any particular stock your profit will be$200, $100,$0 or -$100 (a loss), with probability 0.25 each. There are 100 different stocks you can choose from, and they all behave independently of each other. Consider the 2 cases: (1) Invest$100,000 in one stock. (2) Invest $1000 in each of 100 stocks. a) For case (1) find the probability that your profit will be$8000 or more
b) Do the same for case (2)

So I'm thinking for a) if you invest all $100,000 in one stock it would raise the profits to$20,000, $10,000,$0, or -$10,000, but I don't know how you'd figure out it it'd be$8000 or more? Please help!
In the second case your profit will be the sum of 100 independently identically distributed random variables, so what do you know about such a sum?

CB