Probability question on raffle

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Homework Help Overview

The discussion revolves around a probability problem related to a raffle conducted by a bookstore, where customers draw tickets from a finite pool. The problem involves calculating probabilities under two different scenarios: drawing with replacement and without replacement.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore calculating the probability of winning within a certain number of draws, considering both scenarios of drawing with and without replacement. There are discussions about the odds of not drawing the winning ticket and how to approach the calculations for each part of the problem.

Discussion Status

Some participants have provided calculations and feedback on the accuracy of those calculations. There is acknowledgment of correct reasoning for the first part of the problem, while the second part has prompted further clarification and discussion about the probabilities involved.

Contextual Notes

Participants are navigating the complexities of probability calculations, particularly in distinguishing between scenarios of drawing with and without replacement. There is an emphasis on understanding how probabilities change based on the method of drawing tickets.

BrownianMan
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1 (a) A bookstore has a draw for a $25 book certificate. Each customer draws a ticket from a bowl of 100 tickets. Only one of the tickets is a winning ticket and once the certificate is won, the draw is over. If the tickets are drawn with replacement, what is the probability that the winner is one of the first 10 customers?
(b) If the tickets in part (a) are drawn without replacement, what is the probability that the winner occurs no later than the 99th customer?

Any hints on how to get started?
 
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The easiest way to do this problem is to calculate the odds the lottery goes on for more then ten rounds and use this to get the probability you want. The odds anyone person does not draw the winning ticket (at any point in the lottery) is 99/100. What are the odds ten people all don't win?
 
Last edited:
For part a) I get 0.0956. Is this right?

For part b) wouldn't the probability that the second person doesn't win be 98/99, since the tickets are drawn without replacement?
 
Your first answer is correct. I'm sorry about the second question. You have the right idea for the second problem when you multiply the probibilities lots of terms should cancel.
 

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