Khlara
A class has 3 Teaching Assistants (TAs). Each TA tosses a coin 10 times. Find the chance that at least one of the TAs gets exactly 5 heads.
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dan815
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or in other words what is the probability when no TA gets 5 heads
dan815
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@FibonacciChick666 help us with this
FibonacciChick666
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k so lets make a chart with the outcomes
FibonacciChick666
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strike that cause it will take forever ok what is the probability that 1 TA will get exactly 5 heads?
dan815
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im thinking its like this for 1 TA
dan815
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i dunno im kinda confused about this whole thing
FibonacciChick666
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hmm let me think.... ughh I'm so annoyed we did this in 6th grade why can't I remember...
FibonacciChick666
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at least not all 3 duh ok
FibonacciChick666
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ok so you would think that it would be more likely right
dan815
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hmm
FibonacciChick666
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but coins are weird because the prob for hhhhhh= prob for tthhtt
dan815
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is itt like this
dan815
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for 1 TA getting 5 heads
dan815
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|dw:1367217339549:dw|
FibonacciChick666
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i'm thinking \[the~probability~for~1~TA~is~ (\frac{1}{2})^5\]because they have to be in a row
dan815
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but it says they just need to get 5 outta 10
FibonacciChick666
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oh shoot hmm well that would be one half to the 10th that tells us the total combinations
FibonacciChick666
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then we take out anything that has more than 4 tails
FibonacciChick666
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but we need permutations don't we
dan815
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i think u are right (1/2)^5 for 1 TA
FibonacciChick666
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if that is right then if we cubed it that would be for all three to get it but if we added them that would be for 1 right?
dan815
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that (1/2)^5 * 3 for 1 of the 3 having 5 heads
gotta add the probability of 2 of them getting 5 heads and 3 getting 5 heads
so + [(1/2^5)^2] *3 + [(1/2^5)^3]
dan815
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yeah all probability gotta equal 1
FibonacciChick666
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can't equal one
dan815
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im not sure though if the probability shud be 1/2^5
FibonacciChick666
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neither am I let me call in @hero
dan815
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does that look right for a dice if that is right then i guess u can just use that way for the coin too
FibonacciChick666
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ok... hmm that looks right but i'm just not sure it's been so long since i've taken prob and stats
FibonacciChick666
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you need to learn to write in LaTex...
dan815
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what is that
FibonacciChick666
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but pretty much \[you~write~like~this~for~math~stuff~~~~~~~~~~[\frac{1}{2}]^5\\]
FibonacciChick666
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\[you~write~like~this~for~math~stuff~~~~~~~~~~[\frac{1}{2}]^5\]
dan815
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do you just type that out or use Equation button down there
FibonacciChick666
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type it out
dan815
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o wow lol
FibonacciChick666
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it is a free program for writing in math
FibonacciChick666
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but that is the same as using the eq button down there
dan815
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hbey I THINK I GOT IT NOW
dan815
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|dw:1367219586841:dw|
FibonacciChick666
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the answer cant be one...
dan815
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|dw:1367219732506:dw|
dan815
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no mean 1 - whatever that is equal to is our answer
FibonacciChick666
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ohhhhh uhm maybe i honestly stopped thinking about it
dan815
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i think iam addicted to these questions, i cant stop till i solve when someone asks these questions lol its gonna bug me for ever
FibonacciChick666
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i know but it's 3 am here...
dan815
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so are u on summer vacaation yet
FibonacciChick666
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yep :) for 2 weeks then summer classes you?
dan815
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nice, i got time till summer classes, my summer classes is in 2nd term of summer dunno when that is
FibonacciChick666
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lucky i have like 28 credits over the summer :/
dan815
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wow u took way too much in summer lol
dan815
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how are u gonna keep up! is ur summer term as long as the regular term
FibonacciChick666
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uhm kind of.... i'm not sure though cause i also work like 35 hours a week
dan815
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i dont think id be able to do it, unless its like all electives
dan815
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even then its gotta be some super easy BS on exam electives
FibonacciChick666
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i have PDE, single variable calc proofs, a linguistics intro course, an art class, cog. psych, and more that i forget lol
dan815
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oo PDE :)
dan815
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MATH MAJOR
FibonacciChick666
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ohhh yea should be fun
dan815
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we did some PDE toward the end of this year but i dont think its like indepth as ur PDE class
FibonacciChick666
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yep haha and in the fall i have abstract algebra, ODE, topology or something (math elective) ASL 3 uhmmmand something else haha
FibonacciChick666
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and prob not this class is going to suck massively
dan815
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its gonna be like that Heat equation wave equation and laplace right then using fourier series to solve?
dan815
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thats as far as we got, just doing simple boundary value problems with that
FibonacciChick666
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... were you following me on here tonight? lol
dan815
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whaatt do u mean
FibonacciChick666
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i just answered a PDE on here earlier lol
dan815
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oh haha
dan815
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i just had to cram all that stuff for my exam a couple days ago T_T
dan815
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it was a feather trying to learn fourier series and PDE in 2 days, I was actually gonna give up on the exam.. i went to my mom and was like NO MORE!! I WILL take this in summer
dan815
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but she gave me this huge LECTURE ON stick it out, just believe GOD
FibonacciChick666
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I had linear algebra personally but that sounds dreadful which class?
FibonacciChick666
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...math gods?
dan815
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lol
FibonacciChick666
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I know I usually pray to bolzano or laplace hbu? haha
dan815
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lmao, just Jesus for me :)
FibonacciChick666
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ok if that works for ya haha
dan815
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it dooess!! we seen too much to not believe in god
dan815
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i actually used to be a drug addict and stuff, till I heard God, and my addictions everything even coffee addiction i dunno how lol, just went away over night
dan815
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like my addictions were really really bad, i cudnt control it i cudnt get throught out a day if i wasnt high, not even 5 - 10 mins xD
FibonacciChick666
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thats cool for you and i'm happy you are no longer an addict
dan815
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yep :)
FibonacciChick666
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i am still a firm believer in skepticism however
dan815
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haha thats fine, i wud have never believed it till it finally happened to me
FibonacciChick666
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I was raised wayyyy too catholic, then I started thinking on my own and yep. that is how i am where i am now
dan815
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thats cool
FibonacciChick666
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but oh well, differences aside i think i'm heading to sleep/work so i'll talk to ya again soon and I'll answer this later today when I've slept a little haha
dan815
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okay good night sleep well :)
FibonacciChick666
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Night! and you too!
dan815
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love you lol..
dan815
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saying good night is a very touchy time i feel
NadiaKamal
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HEY THIS IS THE RIGHT ANSWER
NadiaKamal
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he probability of getting 5 heads in 10 tosses =10C5(1/2^5)(1/2^5)=252/1024=0.2461.SIMILARLY the probability of not getting five heads=1-0.2461=0.7539.
now the probability of three students not getting 5 heads =(0.7539)^3=0.4285
so at last the probability of atleast one student get exactly five heads =1-0.4285 which is 0.5715
dan815
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@NadiaKamal :)
dan815
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|dw:1367222891831:dw|
dan815
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|dw:1367222963861:dw|
dan815
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that is the probability for 1 TA getting 5 outta 10 flips as heads
so for atleast 1, or otherwise, inpreted as when none of the TAs get 5 outta 10
= 1-(10 choose 5/2^10) ^3= prob of all 3 TA not getting 5 in a row
so 1- prob of all 3 TA not getting 5 in a row = answer
KABRIC
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THX
KABRIC
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BOTH NADIA AND DAN THX
dan815
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YW:)