Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Left: 1/2 jump to Middle, 1/2 jump to self

Middle: 1/3 jump to Right, 1/3 jump to Left, 1/3 jump to self

How many steps on average is needed from Left to Right?

enter image description here

share|improve this question
add comment

1 Answer 1

up vote 2 down vote accepted

Hint: Let $a$ be the mean number of steps required to get from Left to Right. Let $b$ be the mean number of steps required to get from Middle to Right.

We have $$a=1+\frac{1}{2}a+\frac{1}{2}b,$$ and $$b=1+\frac{1}{3}a+\frac{1}{3}b.$$

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.