New answers tagged probability
1
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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 ...
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2
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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
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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 *...
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1
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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-&...
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12
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11
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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 ...
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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&...
- 11.6k
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 ...
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3
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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 &...
- 11.6k
1
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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 ...
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