A statistics/probability question

Parent Cafe
1

<p>I had lunch with a friend yesterday whose HS son is taking a class which posed the following question, which we both had to concede (sadly) that we could not confidently answer. It has been bugging me ever since, so someone please put me out of my misery and tell me how to figure out answer.</p>

<p>The question is, if I have five raffle tickets and each has a 20 percent chance of winning, what are the chances that I will win something–that is, that at least one of my five raffle tickets will be a winner.</p>

<p>I am sure that I am supposed to multiply something by .20 but I am not sure what . . .</p>

2

<p>If there is only one prize, you must have bought all five tickets in a five-ticket raffle. That is the only way that the probabilities stated in your post could be correct.</p>

<p>Congratulations! You’re a winner!</p>

3

<p>Ha! I think we (the students) are supposed to assume each ticket really could be a winner, so let’s assume there are lots of prizes.</p>

4

<p>There’s something wrong with the question. Perhaps there are many prizes, and 20% of all tickets win at least something.</p>

5

<p>But, if there is more than one prize, then you need more information.</p>

<p>For instance, 100 tickets and 20 prizes is different from 1,000,000 tickets and 200,000 prizes.</p>

<p>It is the draw without replacement formula.</p>

<p><a href=“http://www.regentsprep.org/Regents/math/ALGEBRA/APR2/LpermProb.htm[/url]”>http://www.regentsprep.org/Regents/math/ALGEBRA/APR2/LpermProb.htm&lt;/a&gt;&lt;/p&gt;

6

<p>This is a problem where it is easier to figure out the probability that you don’t win anything, which is (0.8) to the 5th power= 0.32768. The 1st ticket wins nothing and the 2nd and the 3rd… … This is assuming that there are lots of tickets and lots of prizes so that the probability stays relatively constant at 0.8, which is different than probability problems when you have a small counted # of items, like cards or balls of certain colors.</p>

<p>Anyway, the probability that you win at least one item (different from the probability that you win exactly one item) is 1 - .32768 = about 67%</p>

<p>By the way most kids don’t get a chance to do a real probability unit in math in high school unless a teacher works it in for fun. But some basic probability is in the math section of SAT. In particular, they almost always have a problem just like this where it is simple to figure out the ‘opposite’ probability and subtract it from one to get the answer. I was going over it with my D the night before SAT and bingo, it was on the test.</p>

7

<p>celeste - thanks for that explanation. I am wondering why the math does not work the other way. If you start with .2 and ask what is the probability of winning a prize (again assuming enough prizes that the probability stays at 20 percent for all five tickets), you end up with 0.00032.</p>

8

<p>That is the probability that you win 5 prizes. Ticket one wins and ticket 2 wins and …</p>

<p>If you want probability that you win exactly one prize it’s 5x(0.8x0.8x0.8x0.8x0.2)= .41.</p>

<p>One ticket wins, 4 don’t, and that can happen 5 ways. First ticket wins, or 2nd ticket…</p>

9

<p>I suck at math - I was thinking one prize too.</p>

10

<p>Given the info in your question–post #2 is correct.</p>

11

<p>I agree with gouf78, reply #2 is correct given the info in the original post. If you have 5 tickets and each one has 20% chance of winning there are no other tickets and you have 100% chance of winning the prize.</p>

12

<p>gouf78 and wyograd76, well you have to psyche out your teacher. If he’s the type to give trick questions, then you could be right, and given the lack of info in problem, that is one valid interpretation and student could argue such. The other possibility is to assume it’s a real problem that requires work and given what you have the only way to solve is to assume large #s.</p>

13

<h1>2 post sounds right.</h1>

14

<p>I agree with celeste: my first reaction was to assume 10 tix just to make the problem meaningful. As I see the question, it’s asking you to connect odds over iterations: you can see the odds of a single drawing for a single prize so what if there is more than one prize and thus more iterations? </p>

<p>Of course the entire trick of these things is to learn to turn it around, as noted, to focus on 1 minus. I think the trick to doing that, other than remembering it’s the trick, is to think of the whole odds and how you carve your chances out of the whole. That focuses you on how you might lose as well as how you might win.</p>

<p>Much more fun to think of this than bombs.</p>

15

<p>I would tend to agree with celeste, just based on my relatively recent experience as a high school student. </p>

<p>The question is phrased poorly but my guess is that this is the principle that the teacher is getting at.</p>