please help - permutations and probability

Started by jaerob
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jaerob

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Hi everyone-

I suck at permutations and probability questions 🙁 So, I was hoping that some of you guys would be able to help me out with these two problems from Topscore:

1) How many arrangements can six people be seated around a circular table? (the answer is 120.. how come it's not the usual 6*5*4*3*2*1 deal? Is it b/c the table is round and there will be redundancy?)

2) What is the probability of six tails out of nine tosses of a fair coin? (the answer is 21/128)

Oh, help with one geometry problem would be appreciated, too 😀 :

3) Chords AB and CD of Circle O intersect at E. If AE=4, AB=5, CE=2, find ED. (the answer is 2.)

Thanks so much to anyone who can and is willing to help 🙂

-Jae-
 
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jaerob said:
2) What is the probability of six tails out of nine tosses of a fair coin? (the answer is 21/128)
-Jae-
Click to expand...

In my opinion this problem is a bit vague. There are some hidden assumptions..

To get 21/128 one must assume the following:
1) Only 6 tails in 9 tries.
2) You do all 9 tosses even when you get the 6th tail in less than 9 attempts.
3) If you get the 6th tail in less than 9 attempts the rest of the tosses must give you heads.
 
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My version of topscore explained all these problems...just draw an X through the circle and label the chords accordingly, with E as the origin. Then equate (AE)(AB)=(ED)(CD) and solve for the unknown...the others I think you just need to learn and get down cold.
 
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Sorry for all my posts today concerning 'how much detail' we need to go into, but I simply couldn't resist: I've never been good at probability, and I was hoping you could tell me if we really need to study the type of questions that are posted here on this thread...
 
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jaerob said:
Hi everyone-

I suck at permutations and probability questions 🙁 So, I was hoping that some of you guys would be able to help me out with these two problems from Topscore:

1) How many arrangements can six people be seated around a circular table? (the answer is 120.. how come it's not the usual 6*5*4*3*2*1 deal? Is it b/c the table is round and there will be redundancy?)

2) What is the probability of six tails out of nine tosses of a fair coin? (the answer is 21/128)

Oh, help with one geometry problem would be appreciated, too 😀 :

3) Chords AB and CD of Circle O intersect at E. If AE=4, AB=5, CE=2, find ED. (the answer is 2.)

Thanks so much to anyone who can and is willing to help 🙂

-Jae-
Click to expand...

1. You need to use the formula for circular permutation which is (n-1)!
2. Here is another thread
 
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Chords AB and CD both intersect at point E. When this is the case, AE*EB=CE*ED. Thats a theorom. For future refernce, if a chord say is 6 units long, and it is 10 units from the center, then a line from the center to the chord will bissect the chord into two equal parts. Then you can make a right triangle to get the radius of the circle
 
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