MathDB

A coin is tossed

n

times, and the outcome is written in the form (

a_1,a_2,...,a_n

), where

a_i = 1

2

depending on whether the result of the

i

-th toss is the head or the tail, respectively. Set

b_j = a_1 +a_2 +...+a_j

for

j = 1,2,...,n

, and let

p(n)

be the probability that the sequence

b_1,b_2,...,b_n

contains the number

n

. Express

p(n)

in terms of

p(n-1)

and

p(n-2)

Problem Statement