Hey, all! I haven't been here for a long time, but I've got a problem I'm working on, and I'm not quite sure how to present my equation.(adsbygoogle = window.adsbygoogle || []).push({});

My problem is, for any given random event P with 1/D chance of occurring, what is the probability L, given T attempts, of event P occurring at least once?

The probability of P occurring when T is one is obvious, just 1/D, but past that, it seems to get rather complicated.

For D = 2, 3, and 4, the chances are charted below:

Now, I've figured an equation which works for solving for any L in terms of T, but the problem is that it requires the numerator of the previous L, and I don't want to have to get to T = 5 by solving 4, 3, 2, and 1 each time. I'd like an equation that solves for L given only T and D. What's it called if my equation requires a previous result to determine the next result?Code (Text):

D=2

T | L

1 | 1/2

2 | 3/4

3 | 7/8

4 | 15/16

5 | 31/32

D = 3

T | L

1 | 1/3

2 | 5/9

3 | 19/27

4 | 65/81

5 | 211/243

D = 4

T | L

1 | 1/4

2 | 7/16

3 | 37/64

4 | 175/256

5 | 781/1024

I think I put the equation down correctly, please tell me it makes sense.

[tex]L(T) = \frac{N_T}{D_T} = \frac{(D-1)*(N_{T-1})+D^{T-1}}{D^{T}}[/tex]

Did I explain everything all right?

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Attempting to find an equation, not sure how to present it.

Loading...

Similar Threads - Attempting find equation | Date |
---|---|

A very probably flawed attempt at CH | Feb 8, 2012 |

Question on reflexivity, symmetry, and transitivity (Relation on X (Attempt inside)? | Nov 1, 2011 |

Probability of an event is p, average attempt until p happens? | Jun 11, 2011 |

Attempting to find the optimal (exact) solution to TSP | Aug 2, 2008 |

Logical System+new Principles+attempt To Solve Collatz Conjecture | Feb 10, 2008 |

**Physics Forums - The Fusion of Science and Community**