SuicideFuel Problem

[trying to ascend]

[UWSL]A boy in the city of Good Jesus of Pirapora throws a coin. He will walk 1m east if the result is heads or 1m west if the result is tails. The probability that this boy is 5 m away from his starting position after 9 tosses of the coin is[/UWSL]

[UWSL][/UWSL]

 

[Caesercel]

9/64 ?

 

[trying to ascend]

9/64 ?

Correct!

 

[idk125]

what type of questions is this btw

 

[trying to ascend]

what type of questions is this btw

Probability and combinatorics

 

[Caesercel]

Correct!

 

[idk125]

Probability and combinatorics

oh alr looks like a high iq question ngl

 

[NoLooksNoLife]

Pp in vagigi

 

[Deleted member 25223]

Well I could write a program that analyzes the distance for all possibilities and then have it divide the number of instances where the distance was 5 by the total number of 2^9. But that would be too much work. Let's then look at the problem more carefully. First notice that the order of the coins doesn’t matter, so the sequence HTTTTHHHT will yield the same results as the sequence HHHHTTTTT.

Let’s then calculate the chances that he is 5 meters to the west after 9 tosses. This means that his sequence will require 7 Ts and 2 Hs, any sequence like this would do, so how many are there? This is a typical combinatorics problems so we know the answer is 9!/(7!2!) = 9*4. Multiply that by 2 and then divide by the total number of possibilities = (9*8)/(2^9) = 9/(2^6) = 9/64.​