Final answer:
The expected value of entering the sweepstakes, calculated by adding the expected values of each prize, is $0.555, which is less than the $1 cost to enter. Therefore, mathematically, it is not worth entering the sweepstakes.
Step-by-step explanation:
To determine whether it is worth paying a dollar to enter the sweepstakes, we need to calculate the expected value of the game. The expected value is calculated by multiplying each prize by the probability of winning that prize, then summing these values.
The probability of winning the first prize is 1 in 2,000,000, or 0.0000005. Therefore, the expected value from the first prize is $1,000,000 × 0.0000005 = $0.50. Similarly, the expected value from the second prize is $100,000 × 0.0000005 = $0.05, and from the third prize is $10,000 × 0.0000005 = $0.005.
When we add these together, the total expected value is $0.50 + $0.05 + $0.005 = $0.555. Since the cost to enter the sweepstakes is $1, the expected value is less than the cost. Therefore, under these conditions and ignoring other factors such as entertainment value or the unlikely chance of winning, mathematically it's not worth paying a dollar to enter this sweepstakes.