What is the probability of winning with 5 tickets?

  • Thread starter Thread starter Qube
  • Start date Start date
  • Tags Tags
    Probability
Click For Summary

Homework Help Overview

The problem involves calculating the probability of winning a contest with a specific number of tickets. The scenario includes a total of 1,000 tickets, with 5 tickets held by the woman and 2 winning tickets among them.

Discussion Character

  • Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of complementary probability to determine the likelihood of winning. There is a focus on the correct calculation of probabilities involving multiple tickets.

Discussion Status

Some participants have provided guidance on the approach of using the complement, while others have pointed out potential errors in the probability calculations. Multiple interpretations of the calculations are being explored.

Contextual Notes

There is some confusion regarding the correct application of probability rules, particularly in relation to the number of non-winning tickets and the total tickets available. The discussion reflects an ongoing examination of these assumptions.

Qube
Gold Member
Messages
461
Reaction score
1

Homework Statement



A woman has 5 tickets for a contest. There are 1,000 tickets total. Two tickets out of those 1,000 tickets will deem people as winners and they will receive prizes. What is the probability that the woman with the 5 tickets will win a prize?

Homework Equations



Could you find the complement of the event and subtract the probability of the complement from 1?

The Attempt at a Solution



Complement = P(Not getting a winning ticket)

998 non-winning tickets. Probabilities:

1/998 * 1/997 * 1/996 * 1/995 * 1/994 = P(Not getting a winning ticket)

Subtract the above from one.

However, the fact she has five tickets complicates matters; what do I do?
 
Physics news on Phys.org
You already took into account that she has five tickets when calculating the probability she wouldn't have a winning ticket.
 
So I can just subtract the complement from 1?
 
Yup.
 
Oops, you calculated the probability incorrectly. She has 998 ways out of 1000 to pull the first non-winning ticket, not 1 out of 998, and so on.
 
vela said:
Oops, you calculated the probability incorrectly. She has 998 ways out of 1000 to pull the first non-winning ticket, not 1 out of 998, and so on.

You're right. I actually calculated it correctly before I transcribed my work to PF. It's 998/1000 * 997/999 * 996/998 ...
 

Similar threads

Probability of not getting a prize
  • · Replies 36 ·
2
Replies
36
Views
4K
Find the probability of a prize
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Odds of Winning Lottery: Expected Reward & Profit
  • · Replies 8 ·
Replies
8
Views
3K
What Is the Chance a Bookstore Raffle Winner Is Among the First 10 Customers?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Win a $10 or $5 Prize in Tom's 4/19 Lottery Fundraiser
  • · Replies 1 ·
Replies
1
Views
3K
Expected Net Winnings from 1,000 Raffle Tickets
  • · Replies 5 ·
Replies
5
Views
14K
High School Maximize Your Odds: Choosing Winning Lotto Combinations from 1 to 58
  • · Replies 15 ·
Replies
15
Views
6K
Chances of player A winning a chess tournament?
  • · Replies 12 ·
Replies
12
Views
4K
What Is the Probability of Having Enough Seats on an Overbooked Flight?
  • · Replies 3 ·
Replies
3
Views
5K
Undergrad What are the chances of winning a lottery with a group of 52 people?
  • · Replies 2 ·
Replies
2
Views
2K