The table below shows the prizes and probabilities of winning(on a single $1 ticket) for a particular state lottery.
Prize (dollars) Probability
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19 millon(jackpot) 1 in $76,275,360
150,000 1 in 2,179,296
5000 1 in 339,002
150 1 in 9686
100 1 in 7705
5 1 in 220
2 1 in 102
1 1 in 62
How would you expect to win or lose if you bought one $1 ticket every day for a year? Round to the nearest dollar.
Thank you
To determine the expected outcome of buying one $1 ticket every day for a year, we need to calculate the expected value for each prize and probability combination.
The expected value is calculated by multiplying the prize amount by the probability of winning that prize and summing up the results for all possible prizes.
Let's perform the calculation step-by-step:
1. Calculate the expected value for each prize:
- Jackpot (19 million): 19,000,000 * (1/76,275,360)
- $150,000: 150,000 * (1/2,179,296)
- $5,000: 5,000 * (1/339,002)
- $150: 150 * (1/9,686)
- $100: 100 * (1/7,705)
- $5: 5 * (1/220)
- $2: 2 * (1/102)
- $1: 1 * (1/62)
2. Multiply each expected value by the number of days in a year:
- Jackpot: (19,000,000 * (1/76,275,360)) * 365
- $150,000: (150,000 * (1/2,179,296)) * 365
- $5,000: (5,000 * (1/339,002)) * 365
- $150: (150 * (1/9,686)) * 365
- $100: (100 * (1/7,705)) * 365
- $5: (5 * (1/220)) * 365
- $2: (2 * (1/102)) * 365
- $1: (1 * (1/62)) * 365
3. Sum up the results from step 2 to calculate the expected value for the year.
After performing these calculations, you'll have the expected value for buying one $1 ticket every day for a year. Positive values indicate a winning outcome, while negative values indicate a losing outcome.
Please note that rounding to the nearest dollar may affect the final expected outcome, so it's important to keep the exact values during the calculation process and round only at the end.
Typing this out, it mashed everything together but its suppose to read:
Prize(dollars)---------Probabilities
19 million(jackpot)----1 in $76,275,360
and so on.
Thank you