Draft:Disjunctive Probability


References

This is a brief account of disjunctive probability. For details and discussion, see my article “Rewording the Rules on Disjunctive Probability”, Metaphilosophy, Volume 47, Issues 4-5, (October 2016), pages 719-727.

Disjunctive probability deals with the likelihood that a disjunction is true. A statement with “or” is called a “disjunction.” For example, “a or b or c.” Each part of the disjunction is called a “disjunct.” If you know the probability of each disjunct being true, you can figure the probability that the whole disjunction is true.

Sometimes only one of the disjuncts can be true. In such a case, to figure the probability of the whole disjunction being true, you simply add the probabilities for each of the disjuncts.

Suppose, for example, there is a 40% chance she is in London right now, a 10% chance she is in Paris, and a 30% chance she is in Rome. To figure the probability that she is in one of the three, you add the figures. 40% + 10% +30% = 80%. The probability she is in London or Paris or Rome right now is 80%.

Other times more than one of the disjuncts can be true. In such a case, to figure the probability of the whole disjunction being true, you have to figure the chance that it is NOT the case that every one of the disjuncts is false. First you figure the chance of a given disjunct being false by subtracting its probability from 100%. Then you figure the chance that all of the disjuncts are false by multiplying all the chances of falsity together. And then you subtract that figure from 100%.

Suppose, for example, there is a 40% chance she visited London on her trip, a 10% chance she visited Paris, and a 30% chance she visited Rome. First, calculate the probability that each disjunct is false, by subtracting the probability it is true from 100%. The probability she didn’t visit London is 60%, the probability she didn’t visit Paris is 90%, and the probability she didn’t visit Rome is 70%. The probability she didn’t visit any of the cities is found by multiplying the last figures together: 60% x 90% x 70% = 37.8%. There is a 37.8% chance she didn’t visit any of the cities. And the probability that THAT is not the case is 100% - 37.8% = 62.2%. If it is false that she didn’t visit any of the cities, there is a 62.2% probability that she visited at least one.

Content Disclaimer

Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.

  1. The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
  2. There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
  3. It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
  4. Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
  5. Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.