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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 ...
Will Octagon Gibson's user avatar
2 votes

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 ...
mathswithronald's user avatar
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 *...
matt_rule's user avatar
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1 vote

frog on a number line

Consider the set $S$ of all paths from $C$ to $A$, where a path is represented by a concatenation of $B$, $C$, and $D$ ending with $A$. For instance, $BCDCBA$ represents the path $C->B->C->D-&...
Robearz's user avatar
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12 votes

frog on a number line

The answer is because note
Florian F's user avatar
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11 votes

frog on a number line

Let's make every state in the game worth an amount of money to be in: A B C D E $6 $4 $2 $1 $0 With the way that the prices are ...
Misha Lavrov's user avatar
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6 votes

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&...
RobPratt's user avatar
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22 votes
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 ...
Nuclear Hoagie's user avatar
3 votes

Expected number of steps

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 &...
RobPratt's user avatar
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1 vote

Expected number of steps

Partial Answer - Simulation Welcome to this site @12HackingEarth. Those assumptions are made in the simulation (If I understood correctly your challenge): Any car can be selected, independently of ...
10010100102ohno's user avatar

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