<p>Ok--- Some of these are probability/counting principle problems that I wasnt 100% sure about. This is great SAT prep! See if our answers match up!</p>
<p>1.) How many different ways can 13 different runners finish in 1st, 2nd, and 3rd place?
I got 13!/10! = 13x12x11x10!/10! = 1,716</p>
<p>2.) There are 5 people in the math club. How many different 3-person teams can be formed from these 5 students. I got 10 </p>
<p>3.) The next question is rather tedious, but its not too hard
I hope I did it right. ===</p>
<p>17C2x9C7/ 12C11 *** All of the letters should be Sub scripted ... I couldn't figure out how to do that on this computer.... I got 408</p>
<p>4.) Heres one that I had no clue on how to work out
Well, not enough. ===
A state lottery consists of drawing 6 #s from the first 36 possible INTEGERS. Find the probability of winning the lottery. ????</p>
<p>5.) Heres the 2nd problem where I just didnt know where to start. ===</p>
<p>Suppose 2 fair dice are rolled. What is the probability that a SUM of 3 and 9 turns up? ---- You need to know the addition with probability or whatever to get that one. </p>
<p>6.) Ok. In this one, theres a pie diagram in which there are 10 pieces of pie. 5 of them have the letters A B C D and E all in capital letters. The five other slices are labeled f g h i and j, all in lower case letters. The question is Whats the probability of landing on a lower case letter OR a constant
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<p>All help is GREATFULLY appreciated. Thanks everyone!</p>
<p>First post! Yay! </p>
<p>The first three are correct.</p>
<p>4) Assuming that order doesn't matter (as in most lotteries when the numbers are automatically arranged from smallest to largest, or something) and that you cannot have repetition, it is simply 1, divided by 36C6. </p>
<p>5) A sum of 3 and 9, as in the numbers on the two dice add up to a 3 or a 9?-- could you clarify?</p>
<p>6) Again, could you clarify about the "landing on.. a constant" bit?
If the slices are all of equal size and you mean, landing on a consonant, the probabilty is 4/5: there are five lower-case letters, and seven consonants letters, but there are four letters that are both lower-case AND consonants, so by inclusion-exclusion there are 5+7 -4 = 8 letters that work, for a probability of 8 in ten. In other words, if you select A and E, which are neither lower-case or consonants, it doesn't work, so you have a 2/10 chance of failure -> a 1-2/10 = 8/10 chance of success.</p>
<p>5.) Heres the 2nd problem where I just didnt know where to start. ===</p>
<p>Suppose 2 fair dice are rolled. What is the probability that a SUM of 3 and 9 turns up? ---- You need to know the addition with probability or whatever to get that one. </p>
<p>Just consider all the possible combinations of dice that could add up to either 3 or 9, find the probabilities for each of these, and then add them together.</p>
<p>1+2 (=3): (1/6)x(1/6)= 1/36
2+1 (=3): (1/6)x(1/6)= 1/36
3+6 (=9): (1/6)x(1/6)= 1/36
4+5 (=9): (1/6)x(1/6)= 1/36
5+4 (=9): (1/6)x(1/6)= 1/36
6+3 (=9): (1/6)x(1/6)= 1/36</p>
<p>(1/36) + (1/36) + (1/36) + (1/36) + (1/36) + (1/36) = 6/36 = 1/6</p>
<p>I believe that's how you would solve it...</p>
<h1>5 is referring to "using addition with probability." If the event is EXclusive then you use P(a)+P(b) and if they're inclusive events then you use the formula p(a)+p(b)-p(a and b) The question says A SUM of 3 or 9.... So I think zach's right. OH CRAP! It says that it's 3 OR 9. #6 is multiple choice A.) 7/10 b.) 2/5 c.) 1/2 d.) 4/5 --- Thank you both! I know this is a stupid question, but what exactly is a constant? Maybe I didn't spell it right when I typed it and it's something else. Isn't it like a letter that represents something?</h1>
<p>Another concern about "the lottery" question... wouldn't you subtract one in the denominator or something like that? or subtract one from somewhere... I don't know where I heard that info. thanks again.</p>