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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- anonymous

- katieb

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- dan815

or in other words what is the probability when no TA gets 5 heads

- dan815

@FibonacciChick666 help us with this

- FibonacciChick666

k so lets make a chart with the outcomes

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## More answers

- FibonacciChick666

strike that cause it will take forever ok what is the probability that 1 TA will get exactly 5 heads?

- dan815

im thinking its like this for 1 TA

- dan815

i dunno im kinda confused about this whole thing

- FibonacciChick666

hmm let me think.... ughh I'm so annoyed we did this in 6th grade why can't I remember...

- FibonacciChick666

at least not all 3 duh ok

- FibonacciChick666

ok so you would think that it would be more likely right

- dan815

hmm

- FibonacciChick666

but coins are weird because the prob for hhhhhh= prob for tthhtt

- dan815

is itt like this

- dan815

for 1 TA getting 5 heads

- dan815

|dw:1367217339549:dw|

- FibonacciChick666

i'm thinking \[the~probability~for~1~TA~is~ (\frac{1}{2})^5\]because they have to be in a row

- dan815

but it says they just need to get 5 outta 10

- FibonacciChick666

oh shoot hmm well that would be one half to the 10th that tells us the total combinations

- FibonacciChick666

then we take out anything that has more than 4 tails

- FibonacciChick666

5*

- FibonacciChick666

but we need permutations don't we

- dan815

i think u are right (1/2)^5 for 1 TA

- FibonacciChick666

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

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

yeah all probability gotta equal 1

- FibonacciChick666

can't equal one

- dan815

im not sure though if the probability shud be 1/2^5

- FibonacciChick666

neither am I let me call in @hero

- dan815

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

ok... hmm that looks right but i'm just not sure it's been so long since i've taken prob and stats

- FibonacciChick666

you need to learn to write in LaTex...

- dan815

what is that

- FibonacciChick666

http://openstudy.com/study#/groups/LaTeX%20Practicing!%20%3A) you can learn it here

- FibonacciChick666

but pretty much \[you~write~like~this~for~math~stuff~~~~~~~~~~[\frac{1}{2}]^5\\]

- FibonacciChick666

\[you~write~like~this~for~math~stuff~~~~~~~~~~[\frac{1}{2}]^5\]

- dan815

do you just type that out or use Equation button down there

- FibonacciChick666

type it out

- dan815

o wow lol

- FibonacciChick666

it is a free program for writing in math

- FibonacciChick666

but that is the same as using the eq button down there

- dan815

hbey I THINK I GOT IT NOW

- FibonacciChick666

sweet

- dan815

|dw:1367219586841:dw|

- FibonacciChick666

the answer cant be one...

- dan815

|dw:1367219732506:dw|

- dan815

no mean 1 - whatever that is equal to is our answer

- FibonacciChick666

ohhhhh uhm maybe i honestly stopped thinking about it

- dan815

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

i know but it's 3 am here...

- dan815

so are u on summer vacaation yet

- FibonacciChick666

yep :) for 2 weeks then summer classes you?

- dan815

nice, i got time till summer classes, my summer classes is in 2nd term of summer dunno when that is

- FibonacciChick666

lucky i have like 28 credits over the summer :/

- dan815

wow u took way too much in summer lol

- dan815

how are u gonna keep up! is ur summer term as long as the regular term

- FibonacciChick666

uhm kind of.... i'm not sure though cause i also work like 35 hours a week

- dan815

i dont think id be able to do it, unless its like all electives

- dan815

even then its gotta be some super easy BS on exam electives

- FibonacciChick666

i have PDE, single variable calc proofs, a linguistics intro course, an art class, cog. psych, and more that i forget lol

- dan815

oo PDE :)

- dan815

MATH MAJOR

- FibonacciChick666

ohhh yea should be fun

- dan815

we did some PDE toward the end of this year but i dont think its like indepth as ur PDE class

- FibonacciChick666

yep haha and in the fall i have abstract algebra, ODE, topology or something (math elective) ASL 3 uhmmmand something else haha

- FibonacciChick666

and prob not this class is going to suck massively

- dan815

its gonna be like that Heat equation wave equation and laplace right then using fourier series to solve?

- dan815

thats as far as we got, just doing simple boundary value problems with that

- FibonacciChick666

... were you following me on here tonight? lol

- dan815

whaatt do u mean

- FibonacciChick666

i just answered a PDE on here earlier lol

- dan815

oh haha

- dan815

i just had to cram all that stuff for my exam a couple days ago T_T

- FibonacciChick666

yucky

- dan815

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

but she gave me this huge LECTURE ON stick it out, just believe GOD

- FibonacciChick666

I had linear algebra personally but that sounds dreadful which class?

- FibonacciChick666

...math gods?

- dan815

lol

- FibonacciChick666

I know I usually pray to bolzano or laplace hbu? haha

- dan815

lmao, just Jesus for me :)

- FibonacciChick666

ok if that works for ya haha

- dan815

it dooess!! we seen too much to not believe in god

- dan815

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

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

thats cool for you and i'm happy you are no longer an addict

- dan815

yep :)

- FibonacciChick666

i am still a firm believer in skepticism however

- dan815

haha thats fine, i wud have never believed it till it finally happened to me

- FibonacciChick666

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

thats cool

- FibonacciChick666

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

okay good night sleep well :)

- FibonacciChick666

Night! and you too!

- dan815

love you lol..

- dan815

saying good night is a very touchy time i feel

- anonymous

HEY THIS IS THE RIGHT ANSWER

- anonymous

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

@NadiaKamal :)

- dan815

|dw:1367222891831:dw|

- dan815

|dw:1367222963861:dw|

- dan815

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

- anonymous

THX

- anonymous

BOTH NADIA AND DAN THX

- dan815

YW:)

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