Question

Q2: Consider a line axis where there are blocks at position x 3 and x 3 and a point moves along the axis. Every time the point at position x (-3 <x <3) can either move left (x - 1) with probability of 0.5 or move right (x +1) with probability of 0.5. However, it cannot penetrate the block (e.g., at position x 3, if the point keeps moving right, it stays in the same position. This situation still counts one move). Starting from x 0, what is the probability of the point being at position x 0 after 8 moves? left right 3 -2-1 01 2 3

Answer 1

$Let~Y~be~random~variable~denoting~no.~of~moves~in~the~right~side~and\\ since~the~moves~are~independent~so~Y\sim Binomial(8,0.5).\\ x=0~after~8~moves~means~Y=4\\ Hence~required~probability=P(Y=4)=\binom{8}{4}(0.5)^8=0.2734$