What is your expected value for a game whose probabilities and outcomes are given in the following table? Assume the wager is $1.
Proability
0.2 = you win 2 times wager
0.3 = you win your wager
0.3 = you lose 2 times your wager
0.2 = you win nothing
*Having trouble setting up this problem, any help is appreciated.*
0.10? Is this correct?
.2*2 + .3*1 -.3*2 -.2*0
.4 + .3 -.6 - 0
.1
I agree
To calculate the expected value for this game, we first need to multiply each outcome by its corresponding probability and then sum them up.
Let's call the outcomes: a, b, c, and d.
Outcome a: You win 2 times your wager = $2
Probability of outcome a: 0.2
Outcome b: You win your wager = $1
Probability of outcome b: 0.3
Outcome c: You lose 2 times your wager = -$2
Probability of outcome c: 0.3
Outcome d: You win nothing = $0
Probability of outcome d: 0.2
Now, we can calculate the expected value using the formula:
Expected Value = (Outcome a × Probability of outcome a) + (Outcome b × Probability of outcome b) + (Outcome c × Probability of outcome c) + (Outcome d × Probability of outcome d)
Expected Value = (2 × 0.2) + (1 × 0.3) + (-2 × 0.3) + (0 × 0.2)
Expected Value = 0.4 + 0.3 - 0.6 + 0
Expected Value = 0.1
So, the expected value for this game is $0.1.
To calculate the expected value for this game, you need to multiply each outcome by its corresponding probability, and then sum them up.
Let's define the possible outcomes:
A: You win 2 times the wager = 2
B: You win your wager = 1
C: You lose 2 times your wager = -2
D: You win nothing = 0
Now, let's calculate the expected value step by step:
1. Multiply each outcome by its corresponding probability:
A: (0.2)(2) = 0.4
B: (0.3)(1) = 0.3
C: (0.3)(-2) = -0.6
D: (0.2)(0) = 0
2. Sum up the results:
0.4 + 0.3 + (-0.6) + 0 = 0.1
Therefore, the expected value for this game is 0.1.
This means that, on average, for every $1 wagered, you can expect to gain 10 cents.