Answer:
expected payout for case 1: $2.1
expected payout for case 2: $5.5
I prefer the second scenario.
Step-by-step 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.
