TS QR question

[The Godfather]

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Hey guys,
I am lost in the whole probabilities thing. There is a question in the 1st test of TS that reads "What is the probability of six tails out of nine tosses of a fair coin." The answer is 21/128. How do you get that? I know each time you toss the coin there is a 1 in 2 chance of getting either heads or tails, but how do you get to 21/128? I can't seem to find the answer anywhere. Thanks!

 

[busdriver]

it's been too long since i've done probability so i don't know all the definitions and stuff but i can definitely point you in the right direction. basically, to get 6 tails out of 9 tosses means that 6 have to be tails and 3 HAVe to be heads so 1/2 x 9 = 1/512. now you just have to find the combinations of having 6 tails and 3 heads...and i think basically you'll get 9!/(3!)(6!). that should get you 21/128. as to how i knew to do that i'm not sure...and i'm hoping someone can better explain this...but i hope you know what i mean by having to get 6 tails and 3 heads...u can't just get 6 tails alone...

 

[luder98]

This is how I do it:

Total occurences: 2x2x2x2x2x2x2x2x2 = 2^9

Total desired occurences: combination of 6,9: 9!/(3!*6!)=7*8*9/(2*3)=7*4*3

Prob = desired/total = 7*4*3/2^9 = 7*3/2^7 = 21/128

 

[The Godfather]

Thanks a bunch to both of you! That makes complete sense. That's one less thing on my "shaky" list. Looks like I need to dust off that part of my brain for The Test. Six days and counting.