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?

Rationale

The probability of winning from a single lottery ticket is 1/10,000.

In this lottery, a student must match four drawn numbers from a set of ten, where the order does not matter and each draw is independent. The total number of possible outcomes when drawing four numbers is 10^4, which equals 10,000, while there is only one favorable outcome that matches the student's ticket. Thus, the probability of winning is calculated as 1 favorable outcome over 10,000 total outcomes.

A (1/4,000) YOUR ANSWER

This option represents a misunderstanding of the total number of outcomes. With four draws from ten balls, the calculation involves 10^4 possible combinations, leading to a total of 10,000 outcomes, making 1/4,000 an incorrect probability.

B (10-Jan) YOUR ANSWER

This choice appears to be a typographical error or misinterpretation, as "10-Jan" does not represent a numerical probability and does not relate to the correct calculation of winning probabilities in this lottery scenario.

C (1/10,000) CORRECT

This is the correct answer, as it accurately reflects the probability of winning when considering that there is only one winning combination out of 10,000 total possible combinations when drawing four numbers from ten options.

D (04-Jan) YOUR ANSWER

This option seems to suggest a fraction but does not accurately express the probability of winning. The number "4" does not correspond with any correct calculation in the context of drawing four numbers from a set of ten, leading to another incorrect inference.

Conclusion

In summary, the probability of winning the lottery by matching four numbers drawn from a set of ten is 1/10,000. This is derived from the total possible outcomes being 10,000, with only one favorable outcome available. The other choices misrepresent the calculations or fail to convey valid probabilities, reinforcing the importance of understanding the underlying principles of probability in lottery scenarios.

The probability of winning from a single lottery ticket is 1/10,000.

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