Question

@rational decide if you wanna play this game or not .
I toss a coin and you call if you win I give you 200$ if you lose you give me 100$ If I toss 10 times

Answer 1

il play if you let me give you the coin

Answer 2

haha are u sure ?

Answer 3

just want to make sure you're not using a custom made coin with some kind of robotic sensor lol

Answer 4

definitely, the expected value is positive here, so it is always wise to play this game

Answer 5

:P
ur changing ur mind so quick

Answer 6

nope, i said il play the game if you let me give you the coin

Answer 7

oh so u wont let me toss it ?

Answer 8

i want the coin to be unbiased

Answer 9

haha ok so u would give me 200$ in case i guessed right ?

Answer 10

ugh no

Answer 11

lol ok

Answer 12

>.<

Answer 13

haha

Answer 14

success probability = 1/2
failure probability = 1/2

since you're giving me 200 for success, and i just need to give you 100 for failure, il be making profit in the long therm

Answer 15

He wants it to be a fair coin, he is not trying to trade you your fair coin for his unfair coin.

Answer 16

exactly ^

Answer 17

ok @rational i wont play it with u :P
at least i would loose 100$

Answer 18

in 10 tosses, you will be loosing $500 i guess

Answer 19

i said at least 100$

Answer 20

smallest case me to guess wrong 7 times

Answer 21

worst case to guess wrong 10 times i would lose 1000$

Answer 22

if it is your lucky day, you might win all 10 tosses! who knows!

Answer 23

im lucky in those games :P

Answer 24

unless you are capable of flipping with identical spins of the coin...

Answer 25

then you may have an issue ;P

Answer 26

hahaha if i flip the coin i can know what it is without looking xD

Answer 27

yep. I know the trick too :)

Answer 28

hehe

Answer 29

i use number theory in that trick (even odd ) case xD

Answer 30

you want to find probability of making profit ?

Answer 31

sure

Answer 32

this is also a binomial distribution

Answer 33

yeah i would like to learn it

Answer 34

I need to win at least 4 tosses to make profit, yes ?

Answer 35

yes

Answer 36

By winning 4 tosses, il be getting 4*200 = 800
after that even if loose all remaining tosses, il be only giving you 6*100 = 600

il be making 200 profit

Answer 37

so simply find the probability of P(X >= 4)

Answer 38

http://www.wolframalpha.com/input/?i=+sum%28binomial%2810%2Ck%29+%281%2F2%29%5E%7Bk%7D+%281%2F2%29%5E%2810-k%29++%29+from+k%3D4+to+10

Answer 39

there is one thing good about tossing coin
its black and white property lol
like p(win)=p(lose) (for first time )
so its always easy to calculate

Answer 40

the probability of making profit for me is 53/64 which is pretty huge !

Answer 41

yes of losing it was 11/64

Answer 42

dou know that binomial distribution is derived from beta function ?

Answer 43

never took statistics seriously
im familiar wid beta function, so it does look interesting... teach me how to derive it

Answer 44

\[B(m,n) = \int\limits_0^1 x^{m-1}(1-x)^{n-1}~dx\]

Answer 45

Ahh i see.. this gives the area under binomial distribution curve ?

Answer 46

yes now chance limits of integral to 0-(1-p) and see what u would got

Answer 47

almost yes

Answer 48

it gives the whole area

Answer 49

step by step please

Answer 50

do we need to treat "x" as probability of success and "1-x" as probability of failure ?