### Abstract

We study the multi-selection version of the so-called odds theorem by Bruss (2000). We observe a finite number of independent 0/1 (failure/success) random variables sequentially and want to select the last success. We derive the optimal selection rule when m (≥ 1) selection chances are given and find that the optimal rule has the form of a combination of multiple odds-sums. We provide a formula for computing the maximum probability of selecting the last success when we havemselection chances and also provide closed-form formulae for m = 2 and 3. For m = 2, we further give the bounds for the maximum probability of selecting the last success and derive its limit as the number of observations goes to ∞. An interesting implication of our result is that the limit of the maximum probability of selecting the last success for m = 2 is consistent with the corresponding limit for the classical secretary problem with two selection chances.

Original language | English |
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Pages (from-to) | 1093-1104 |

Number of pages | 12 |

Journal | Journal of Applied Probability |

Volume | 47 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2010 Dec 1 |

### Keywords

- Multiple selection chances
- Optimal stopping
- Selecting the last success

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty

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## Cite this

*Journal of Applied Probability*,

*47*(4), 1093-1104. https://doi.org/10.1239/jap/1294170522