<p>I didn't see this one on the consolidated list of answers. Here's the Question:</p>
<p>A list of numbers consists of "p" positive and "n" negative numbers. If a number is picked at random from this list, the probability that the number is positive is 3/5. What is the value of "n/p"?</p>
<p>A 3/8
B 5/8
C 2/3
D 3/2
E 8/3</p>
<p>I thought I was just getting the hang of probability until I saw one like this. It seems as though the only probability problems I've seen are ones where you are given original amounts and you have to find the probability. I've never seen one where you have to work backwards from the probability to get an original amount in order to find a value. Can someone tell me how to do this one and a process for doing working backwards type probability problems like this that'll work every time?</p>
<p>well its asking you for the number of negative number over the number of positive number. keep in mind it is not asking for negative number over the total number. best way i do it is just plug in numbers. for ex. i used 15, 3/5 of 15 is 9 so i have 9 positive numbers. that means i have 6 negative numbers. the question is asking for negative numbers over positive numbers so you have 6/9 simplify n u get 2/3</p>
<p>obsessedAndre -
Generally you get a wrong answer if you under-read the question.</p>
<p>This question does not state that there are 5 numbers altogether.
Without applying the probability formula (favorable/total), how would you know that 3/5 of numbers on the list are positive?</p>
<p>Swatman888 implicitly based his solution on this fact. He used 15 as a total number of numbers; actually, any multiple of 5 would work. </p>
<p>Say, 20 total. (3/5)x20 = 12 positive numbers. p=12, n=8, n/p=2/3.
(Chances of picking a positive number 12/20 = 3/5).</p>
<p>5 total was your choice for plugging in numbers, but you luckily got the right answer starting with the wrong assumption:
[quote]
it tells you there are 3 p out of a total 5 numbers
[/quote]
</p>
<p>What if a question were more difficult:</p>
<p>A list of numbers consists of "p" positive and "n" negative numbers.
If two numbers are picked at random from this list, the probability that both numbers are positive is 3/10. What is the value of "n/p"?</p>
<p>Will 10 be a total number on the list?</p>
<p>(Coming up with a better solution is commendable. Acting superior is not.)</p>
<p>I don't know...I think obsessedAndre's solution works, although not in the problem you mentioned, gcf101. That's how I looked at it too...although let me try explaining it differently.</p>
<p>Ratio is basically numerator and denominator times x, so 3x/5x is probability of positive number, and 3x is the amount of positive numbers. Then 2x/5x is the probability of picking a negative number, so 2x is the number of negative numbers. 2x/3x = 2/3. That's basically the same thing as Andre said, just expressed mathematically.</p>
<p>evilmonkey32 -
Your solution makes perfect sense - and you are using the probability formula, as opposed to what Andre said:
[quote]
You don't need a formula.
[/quote]
You are using 5x as a total number, and I did the same:
[quote]
any multiple of 5 would work.
[/quote]
I need to make a correction though to my question: A list of numbers consists of "p" positive and "n" negative numbers.
If two numbers are picked at random from this list, the probability that both numbers are positive is 3/10. What is one of the possible values of "n/p"?</p>
<p>And a comment: this kind of a question will never show up on the SAT.</p>
<p>Hmmm, I don't know why this problem has to be made more complex than it really is. And, FWIW, I have to support Andre simple approach. P is known and so is P+N. This means that N is known. There is no need to go further than than 3 + N = 5 or 3 + 2 = 5. </p>
<p>The problem statement, "A list of numbers consists of "p" positive and "n" negative numbers. If a number is picked at random from this list, the probability that the number is positive is 3/5. What is the value of "n/p"?"</p>
<p>is not much different from rephrasing it as "If five numbers are either positive OR negative numbers, and you remove ALL of the three positives ones, how many negatives number are there?</p>
<p>or even simpler, "A bag contains five balls that are red or blue. If you remove ALL of the three red balls, how many blue balls are there? </p>
<p>There is a reason the SAT is known to test all materials from K to 12. In this case, it just happens to be a K problem.</p>
<p>Wow. This problem has been made a lot easier, but sad to say...mostly since I misread the question :(</p>
<p>I read it after just doing several practice problems where probability is taken using two numbers, so I read it to say that two numbers are taken from a set and are multiplied (a case of reading what you want to read), opening up many possibilities. I guess I learned that I must be even more careful when doing these problems. I could've probably gotten a 750 on a practice test but because I read problems the wrong way I got a 700.</p>
<p>xiggi -
I am posting this not because I feel like I need to redeem myself.
It's important to have a complete clarity in a way one should approach the original question:
[quote]
A list of numbers consists of "p" positive and "n" negative numbers. If a number is picked at random from this list, the probability that the number is positive is 3/5. What is the value of "n/p"?
[/quote]
This is how you rephrased it:
[quote]
"If five numbers are either positive OR negative numbers, and you remove ALL of the three positives ones, how many negatives number are there?
[/quote]
These two questions are not equivalent because you are not given values either P or P+N.</p>
<p>Based on the probability formula (which, according to Andre, is not needed), it might be that P+N=5 and P=3, because P+N has to be a multiple of 5, and P - a multiple of 3 (with the same factor). Then N=2, N/P=2/3. This is what optimizerdad did: see post #2. It works.</p>
<p>Were we given a restriction on P, or N, or both, it could be a different story: A list of numbers consists of "P" positive and "N" negative numbers. There are 2 more positive numbers than negative ones. If a number is picked at random from this list, the probability that the number is positive is 3/5. What is the value of "N/P"?
You can't assume now that P=3 and P+N=5. You'll get N=2, but then P isn't = N+2.</p>
<p>P=6, P+N=10, N=10-6=4. P is = N+2. Yay!
N/P=2/3.</p>
<p>GCF, I understand what you are saying and no redeeming is needed. </p>
<p>The reduction of the fraction or subtitution of numbers can occur at any time. However, it is better to do it at THE beginning. While it is true that n will NOT always be 2 (if playing with different expressions of the SAME fraction), it will ALWAYS be 2 IF and only IF p is 3 and p+n is 5 ... and that WAS in the problem statement. </p>
<p>However, take a look at this list:</p>
<p>p / (p+ n) = 3/5
p / (p+ n) = 6/10
p / (p+ n) = 9/15
p / (p+ n) = 12/20</p>