Question

You get one lottery ticket that will 5% of the time pay out $5, will 10% of the time pay out $10, and will 85% of the time pay out $1. 2. You get two lottery tickets, A and B. Ticket A will pay $5 half of the time and $0 otherwise. Ticket B will pay double your winnings from ticket A half of the time; otherwise ticket B pays $1. Calculate the expected value (expected payout) of both scenarios. Which would you prefer? Explain why.

Answer 1

expected payout for case 1: $2.1

expected payout for case 2: $5.5

I prefer the second scenario.

Explanation:

First scenario:

- you get paid $5 with probability 0.05

- $10 with probability 0.1

- $1 with probability 0.85

So the expected value is

E = 5*0.05+10*0.1+1*0.85 = 2.1

Second Scenario:

- you get paid $5 from A and $10 for B (a total of $15) with probability 0.25 (this is, if B doubled the value of A)

- you get paid $5 from A and $1 from B (a total of $6) with probability 0.25

-you get paid $0 from A and $0 from B with probability 0.25

- you get paid $0 from A and $1 from B with probability 0.25

Hence the expected value in this case is

E = 15*0.25+6*0.25+0*0.25+1*0.25 = 5.5

Even though in the second scenario you are more likely to gain less money (for one try), the expected value is much higher, so i prefer the second scenario.