Playing game of chance and pay 300 by rolling a fair die one time if you rome a 2 and receive $1300 if you roll a 4 or six you receive $900 if you ore a 3 5 or 9 receive nothing. find expected value for this game. based on value is it a good game to play?
Possible typo in bold:
"Playing game of chance and pay 300 by rolling a fair die one time if you rome a 2 and receive $1300 if you roll a 4 or six you receive $900 if you ore a 3 5 or one receive nothing. find expected value for this game. based on value is it a good game to play?"
If x and P(x) represents the winning amount and P(x) the probability for a particular outcome, then
ΣxP(x) represents the expected value of the game, i.e. expected amount of winnings averaged over a large number of trials.
Outcome x P(x) xP(x)
1 -300 1/6 -50
2 1300-300 1/6 166.67
3 -300 1/6 -50
4 900-300 1/6 100
5 -300 1/6 -50
6 900-300 1/6 100
ΣxP(x)=-50+200-50+100-50+100=216.67
The expected value (winning) is $216.67
To find the expected value for this game, we need to calculate the probabilities and payoffs for each possible outcome, and then take the sum of the products of these probabilities and payoffs.
Let's start by finding the probability of each outcome when rolling a fair die:
- The probability of rolling a 2: 1/6
- The probability of rolling a 4 or 6: 2/6 (since there are two favorable outcomes)
- The probability of rolling a 3, 5, or 9: 3/6
Next, let's calculate the corresponding payoffs for each outcome:
- If you roll a 2, you pay $300 (negative $300).
- If you roll a 4 or 6, you receive $900.
- If you roll a 3, 5, or 9, you receive nothing (negative $0).
Now, we can calculate the expected value:
Expected Value = (Probability of 2) × (Payoff of 2) + (Probability of 4 or 6) × (Payoff of 4 or 6) + (Probability of 3, 5, or 9) × (Payoff of 3, 5, or 9)
Expected Value = (1/6) × (-$300) + (2/6) × ($900) + (3/6) × (-$0)
Expected Value = (-$50) + ($300) + ($0)
Expected Value = $250
The expected value for this game is $250.
Now, to determine whether it's a good game to play, we need to compare the expected value to the cost of playing. In this case, you need to pay $300 to play the game. Since the expected value ($250) is less than the cost of playing ($300), it is not a good game to play from a purely financial standpoint.