Question

A man takes a step forward with probability $0.4$ and backward with probability $0.6$. Let $k$ be the probability that at the end of eleven steps he is one step away from the starting point.Find the first digit after the decimal of $k$ ?

Answer 1

$Eitherhetook6forwardstepsand5backwardstepsor6backwardstepsand5forwardsteps=11C6\ast (0.4{)}^6\ast (0.5{)}^5+11C6\ast (0.4{)}^5\ast (0.6{)}^5=11C5\ast (0.4{)}^5\ast (0.6{)}^5\ast (0.4+0.6)...[11C6=11C5]=(11\ast 10\ast 9\ast 8\ast 7)/(1\ast 2\ast 3\ast 4\ast 5)\ast (0.24{)}^5=\mathrm{0.368.}$