# Confusing in Random Walk

I have a question about of random walk.

Consider a particle starting its random walk at 0. At each step, it either moves in positive or negative direction. If the probability of moving in positive direction is 0.6, what is the probability that it will end up at +1 after 5 steps?

Your question is simpler. Your net movement is $$1$$ to the right, one such situation is $$LLRRR$$, another is $$LRRLR$$,... so, you need $$2L$$ and $$3R$$ irrespective of the order. The probability of a particular $$2L,3R$$ move is $$(0.6)^3(0.4)^2$$. And, there are $${5 \choose 2}$$ such situations, yielding $${5 \choose 2}(0.6)^3(0.4)^2$$. It's the same as having $$3$$ heads in 5 coin tosses.