Solved

Probability: jackpots

Posted on 2010-11-25
5
283 Views
Last Modified: 2012-05-10
I'm stumped by a probability issue I'm trying to work out whilst coding.  My math isn't up to the task!  In simplest terms it could be worked out to this fictional scenario:

Jack bought raffle tickets for three different draws.  Due to the total number of tickets sold for each draw he knows that:
He has a 1/4 chance of winning Game 1
He has a 1/8 chance of winning Game 2
He has a 1/16 chance of winning Game 3

What is his overall chance of winning something (at least one draw)?

When I did 1/2 chance for each draw and played with some numbers, I figured out through trial and error it was around 87.5%, but I can't arrive at the number elegantly, and I certainly haven't figured it out when each draw has a different chance.  Help!
0
Comment
Question by:tknudsen-qec
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
5 Comments
 
LVL 58

Expert Comment

by:cyberkiwi
ID: 34214051
You need to draw a Venn diagram to see this, there will be 7 sections.
The ONLY section that doesn't win anything is
doesn't win game1 AND doesn't win game2 AND doesn't win game3
This is easily calculated as
3/4 * 7/8 * 15/16
0
 
LVL 58

Accepted Solution

by:
cyberkiwi earned 500 total points
ID: 34214056
Oh, and the complement of that (1- the above) will be the probability of winning something.
For reference, your 1/2, 1/2, 1/2 is solved the same way

P(win something) = 1 - (1 - 1/2) x (1- 1/2) x (1 - 1/2) = 1 - 0.125 = 0.875 (or 87.5%)
0
 
LVL 53

Expert Comment

by:Huseyin KAHRAMAN
ID: 34214081
He has a 1/4 chance of winning Game 1 = 3/4 losing
He has a 1/8 chance of winning Game 2 = 7/8 loosing
He has a 1/16 chance of winning Game 3 = 15/16 loosing

(3/4)*(7/8)*(15/16) = 0.6152

so he will not get anything %61.52 and get 1- 0.6152 = 0.3847, %39.47 somehing...
0
 
LVL 3

Author Closing Comment

by:tknudsen-qec
ID: 34214088
Thank you so very much, this is extremely helpful and appreciated.
0
 
LVL 3

Expert Comment

by:babesia
ID: 34214098
As cyberkiwi said.

P(win something) = 1 - (1 - 1/4) x (1- 1/8) x (1 - 1/16) = 1 - 0.615234375 = 0.38476525
0

Featured Post

Industry Leaders: We Want Your Opinion!

We value your feedback.

Take our survey and automatically be enter to win anyone of the following:
Yeti Cooler, Amazon eGift Card, and Movie eGift Card!

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Title # Comments Views Activity
Frequency distribution 6 56
Probability Distribution 2 92
Just learning algebra / need solution explained 4 82
find Speed using GPS latitude & longitude 4 160
How to Win a Jar of Candy Corn: A Scientific Approach! I love mathematics. If you love mathematics also, you may enjoy this tip on how to use math to win your own jar of candy corn and to impress your friends. As I said, I love math, but I gu…
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…

739 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question