Answer :
Final answer:
The correct option is a. Potential Winnings: $7, $6, -$1 Probabilities: 1/20, 2/20, 17/20. The potential winnings for rolling a fair 20-sided die in this game are $7, $6, and -$1, with the probabilities of these outcomes being 1/20, 2/20, and 17/20 respectively.
Explanation:
The question asks about the potential winnings and probabilities for a player in a game involving rolling a fair 20-sided die with specific outcomes. Here is a breakdown of the possible outcomes:
- If they roll a 4, they win $7.
- If they roll an 8 or 18, they win $6.
- If they roll any other number, they lose.
For the potential winnings, we have three distinct possibilities: winning $7, winning $6, and losing (which we'll represent as -$1). Now, for the probabilities:
- The probability of rolling a 4 (thus winning $7) is 1 out of 20, or 1/20.
- The probability of rolling an 8 or 18 (thus winning $6) covers two specific outcomes out of 20, making it 2/20 or 1/10.
- Since there are 17 other numbers that neither win $7 nor $6, the probability of losing (or rolling any other number) is 17/20.
Putting it all together, the correct answer is:
Potential Winnings: $7, $6, -$1
Probabilities: 1/20, 2/20, 17/20
