Standing on the Corner, Tossing A Coin

Anne is standing on the corner tossing a coin. She decides she will toss it 12 times, each time walking 1 block north if it lands head up and 1 block south if it lands tails up. Find the probability that she will end up in the indicated location.

I chose .5 as it appeared to me, 1/2 times chance coin flip heads or tails and she'd be walking forward and backwards exactly the same amount of times per chance, and she'd end up on her corner.

the other choices were 0.1934, 0.0156 and 0.2256. All of which, if I could figure out how to arrive at any of the above choices, I'd know. HELP???, please?

How many ways can you arrange NNNNNNSSSSSS?
That is she has as many norths as souths.
That number is \(\displaystyle \L \frac{{12!}}{{\left( {6!} \right)^2 }}\)
The probability of that happing is \(\displaystyle \L \frac{1}{{\left( 2 \right)^{12} }}\).
Multiply.

did you just randomly pick 12? or does a corner have 12?

when i multiply, i get 2.44140625^-04

that's not one of the choices for an answer!

\(\displaystyle \L\frac{{12!}}{{\left( {6!} \right)^2 \left( {2^{12} } \right)}} = 0.2255859373\)

wow, you're good. i guess when you're good, you're good pka, what are the chances of that!

at least you believe god made man, means you're way ahead of the game

"But is it probable" asked Pascal "that probability gives assurance? Nothing gives certainty but truth; nothing gives rest but the sincere search for truth." When Pascal wrote that, he had gone to live at the Jansenist convent of Port-Royal after a carriage accident in 1654.

Pascal's notes on Christianity were collected after his death in the Pensees (thoughts). The above quotation is included. Another develops Pascal's "rule of the wager": If you bet God exists and live accordingly, you will have gained much even if God does not exist; if you bet the opposite and God does exist, you will have lost the reason for living right - - hence everything.

pka is not perfect: .2255859375 :roll:

Denis said:

pka is not perfect: .2255859375

Click to expand...

hay Denis what clunky software are you using?
Tell us is it better than MathCad?