Post Probability and Counting problems here...

Test Preparation SAT Preparation
1

<p>Okay, as I mentioned in one of the other threads, probability and counting problems tend to screw me up on the Math section(s). I am sure I'm not the only one out there who experiences this screwup. Post any problems you come across while practicing. We could discuss them together. </p>

<p>Note: If you know the answer to the question, please space it out (like 2-3 lines) from the question before posting it. I would like to try the question myself before glancing at the answer. Thanks! :)</p>

<p>I'll start:
In a batch of 20 eggs, 4 are broken. If 6 of the eggs are chosen at random, what is the probability that at least 2 of the chosen eggs are broken?</p>

<p>How do you this? O.o</p>

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<p>im not 100% sure but since it's at least 2 eggs, you find the probability of 1 egg and 0 egg being broken then u subtract that from 1.</p>

<p>0 egg- .8^6 = .262~</p>

<p>1 egg- (.8^5) * (.2^1) * 6C1 (combination) = .393~</p>

<p>1 - .262 - .393 = .345</p>

<p>So theres around a 34.5% chance that at least 2 eggs are broken if 6 eggs are chosen at random. But like i said I dunno if i did it right...but anyways is that even a real sat problem?</p>

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<p>

[quote="voodoo_santa, post:2, topic:10"]

but anyways is that even a real sat problem?

[/quote]
</p>

<p>I hope not.</p>

4

<p>Ahem, not to stress you out or anything, but this is a real SAT problem.
It's in Barron's ... I'm too lazy to go look up the page no.</p>

<p>So, anyone know for sure how to do this?
(Thanks, voodoo_santa :))</p>

5

<p>Voodoo_santa's got the right idea. </p>

<p>The probability that none of the eggs are broken is the number of ways to choose 6 of the unbroken eggs over the number of ways to choose any six eggs. </p>

<p>In other words, it's 16C6 / 20C6, where C represents combinations - you should know how to do these. </p>

<p>The probability that exactly one egg is broken is equal to </p>

<p>16C5 * 4C1 / 20C6</p>

<p>That is, the number of ways to chose 5 unbroken eggs times the number of ways to chose 1 broken egg, over the total number of ways to choose any six eggs. </p>

<p>Add up the two probabilities and subtract from one. You've got a calculator, so this should be fairly straightforward.</p>

6

<p>This is definitely not a real SAT problem; while you should be familiar with basic probabilities, they will not expect you to do something as complex as this. Barron's is focused on helping you learn the concepts at a more advanced level in order to boost your confidence and performance on easier problems that will appear on the SAT.</p>

7

<p>Okay, I went back to the book, and looked up where it exactly was.
Begoner's right. :)
It's only for <em>extended practice</em>, and not a real problem on one of the practice tests.</p>

<p>I'm sorry guys. Didn't mean to cause trouble or anything.
Also, thank you Voodoo_santa and javademon, I think I sort of got the problem. :)</p>