Answer :
Answer:- P(any other outcome) = 3/6 (as there are 3 outcomes remaining: 1, 2, 3, each with 1/6 probability)
Now, we calculate the expected value:
Expected winnings = (P(rolling a 6) $7) + (P(rolling a 5) $3) + (P(rolling a 4) $2) + (P(any other outcome) $0)
Expected winnings = ($7/6) + ($3/6) + ($2/6) + ($0)
Expected winnings = $1.17 + $0.50 + $0.33 + $0
Expected winnings = $2
Therefore, the expected winnings for this game are $2.
Step-by-step explanation: To find the expected winnings for this game, we need to calculate the expected value. The expected value is calculated by multiplying each outcome by its probability and then summing up these values.
Given payouts:
- $7 for rolling a 6
- $3 for rolling a 5
- $2 for rolling a 4
- No payoff for any other outcome
To find the probabilities of each outcome, we know that a fair die has 6 sides, each with an equal probability of 1/6.
So, the probabilities are:
- P(rolling a 6) = 1/6
- P(rolling a 5) = 1/6
- P(rolling a 4) = 1/6
- P(any other outcome) = 3/6 (as there are 3 outcomes remaining: 1, 2, 3, each with 1/6 probability)
Now, we calculate the expected value:
Expected winnings = (P(rolling a 6) $7) + (P(rolling a 5) $3) + (P(rolling a 4) $2) + (P(any other outcome) $0)
Expected winnings = ($7/6) + ($3/6) + ($2/6) + ($0)
Expected winnings = $1.17 + $0.50 + $0.33 + $0
Expected winnings = $2
Therefore, the expected winnings for this game are $2.
