Final answer:
The probability of winning the Ohio Lottery Pick 4 game is 1/10,000, as there are 10 possible numbers for each of the four positions, and they must be in the exact order.
Step-by-step explanation:
The Ohio Lottery Pick 4 game involves selecting a four-digit number with the hope that it matches the number drawn by the lottery. When we consider the probability of winning, it's important to think of each individual digit. Since there are 10 possible numbers for each digit (0 through 9), and since you must get all four numbers correct and in the exact order, we calculate the probability by multiplying the probability of each individual selection. As the drawing is with replacement, the probability for each digit remains 1/10. Therefore, the probability of winning is (1/10) * (1/10) * (1/10) * (1/10), which is 1/10,000 or 0.0001 when we express it in decimal form. When your chance of winning is this low, the prize being $3,200 does tempt players, but the odds are clearly stacked against them.