19. A college hosts a lottery using balls numbered 1 through 10. Four ×, a ball is drawn with replacement. If all four numbers drawn match the numbers that someone has on the lottery ticket, the student wins a semester's tuition. The order of the numbers does not matter. What is the probability of winning from a single lottery ticket?
Answer: C
The probability of winning from a single lottery ticket is 1/10,000.
To determine the probability of winning, we consider that there are 10 balls numbered from 1 to 10, and four balls are drawn with replacement. The winning ticket must match all four numbers drawn, and since the order does not matter, we find that the probability of winning from a single ticket is 1/10,000.
A) 1/4,000
This option is incorrect because the calculation for matching four specific numbers out of ten, regardless of order, does not yield a probability of 1/4,000. The total combinations of four numbers from ten, considering the drawing is with replacement, leads to a lower probability.
B) 10-Jan
This option is not a valid probability format and does not represent any calculable probability. Therefore, it cannot be considered correct.
C) 1/10,000
This is the correct answer. The probability of drawing any specific combination of four numbers from ten is 1 divided by the total combinations possible, which is 10^4 (or 10,000), resulting in a probability of 1/10,000.
D) 04-Jan
Similar to option B, this is not a valid probability format. The expression does not correspond to a numerical probability and hence is not correct.
Conclusion
The correct answer of 1/10,000 accurately represents the probability of winning based on the total number of possible outcomes when drawing four balls with replacement from a set of ten. Other options either incorrectly represent probabilities or are not in a valid format, confirming that C is the only correct choice.