# Tag Info

1 vote

### frog on a number line

The probability that the frog stops at A after two jumps is $\frac{1}{3} \times \frac{1}{2} = \frac{1}{6}$. The probability that the frog lands at C after two jumps is $\frac{1}{2}$ because no matter ...

### frog on a number line

Let $p$ be the probability that a frog standing on C ultimately reaches A, as required. This probability $p$ will therefore apply both to a frog starting out its journey, and to a frog who has ...
1 vote

### frog on a number line

This already has a solution but for the sake of variety, here's a numerical solution in Google Sheets (also applicable to Excel). Numerical solution 1: Trace from A to C A B C D E 1 0 0 0 0 1 =1/2 *...
1 vote

### frog on a number line

The transition probability matrix is  P = \begin{pmatrix} 1& 0& 0& 0& 0\\ 1/2& 0& 1/2& 0& 0\\ 0&...
Accepted

### frog on a number line

It's easy to see by transforming the problem into a symmetric one - instead of a 1/3 vs. 2/3 jump to B or D, make a third branch so it's a uniform 1/3 chance of going to B, D, or D' (which in turn has ...
Here are the first $10$ values, obtained via a Markov chain with $\binom{2N}{N}$ states, one for each placement of $N$ cars in $2N$ spots: \begin{matrix} N & \text{expected number} \\ \hline 1 &...