Probability Problem: 2 Ticket Draw, What's the Odds?

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Homework Help Overview

The problem involves drawing two tickets from a box containing tickets numbered from 1 to n, and seeks to determine the probability that the second ticket drawn has a higher number than the first. The original poster expresses confusion regarding a provided answer and seeks clarification on the reasoning behind it.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of the provided answer and question its validity, particularly in the context of different values of n. There is also a discussion about the nature of the probabilities involved when considering the order of the draws.

Discussion Status

The discussion is active, with participants questioning the correctness of the provided answer and exploring different scenarios, such as sampling with and without replacement. Some participants are seeking further clarification on the relationship between the probabilities of the two draws.

Contextual Notes

Participants note that the problem involves sampling with replacement, which may influence the calculations and interpretations of the probabilities. There is also mention of a potential misunderstanding regarding the nature of complementary probabilities.

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A box contains tickets marked 1,2,...,n. Two tickets are drawn at random from the box. What is the probability the second number drawn is bigger than the first number drawn?
The answer shown is (1-1/n)/2. But... how?

Thanks in advance!
 
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What happens when n = 2?
 
Tide's point is that the "answer shown" is WRONG. It shouldn't take a whole lot of thought to see that the probability that "the second number drawn is bigger than the first number" is exactly the same as the probability that "the first number drawn is bigger than the second number.
 
Just out of curiosity, where did you get that formula?
 
Sorry to all, forgot to mention that this is "sampling with replacement". So, by using HallsofIvy's hint, I know how to derive it now. Thanks! And just curious, the answer for without replacement is 1/2?

HallsofIvy, can you give more explanation on "the second number drawn is bigger than the first number" is exactly the same as the probability that "the first number drawn is bigger than the second number"? they sound more like compliments to me with one higher and one lower probability...
 
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