Polybutylene water pipes are no longer accepted by the United States building codes and have been the subject [16] of class action lawsuits in both Canada and the U.S. [17] [18] The National Plumbing Code of Canada 1995 listed polybutylene piping as acceptable for use with the exception of recirculation plumbing. The piping was removed from the acceptable for use list in the 2005 issue of the standard. [19]

There is evidence to suggest that the presence of chlorine and chloramine compounds in municipal water (often deliberately added to retard bacterial growth) will cause deterioration of the internal chemical structure of polybutylene piping and the associated acetal fittings. [22] The reaction with chlorinated water appears to be greatly accelerated by tensile stress, and is most often observed in material under highest mechanical stress such as at fittings, sharp bends, and kinks. Localized stress whitening of the material generally accompanies and precedes decomposition of the polymer. In extreme cases, this stress-activated chemical "corrosion" can lead to perforation and leakage within a few years, but it also may not fail for decades. Fittings with a soft compression seal can give adequate service life. [ further explanation needed] Polybutylene (Poly-B) Pressure Water Piping" (PDF). municipalaffairs.alberta.ca. Government of Alberta. 2012-01-06 . Retrieved 2019-09-09. Definition [ edit ] Illustration of conditional probabilities with an Euler diagram. The unconditional probability P( A) = 0.30 + 0.10 + 0.12 = 0.52. However, the conditional probability P( A| B 1) = 1, P( A| B 2) = 0.12 ÷ (0.12 + 0.04) = 0.75, and P( A| B 3) = 0. On a tree diagram, branch probabilities are conditional on the event associated with the parent node. (Here, the overbars indicate that the event does not occur.) Venn Pie Chart describing conditional probabilities Conditioning on an event [ edit ] Kolmogorov definition [ edit ]

P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∩ B ) {\displaystyle P(A\cup B)=P(A)+P(B)-P(A\cap B)} Thus the equations can be combined to find a new representation of the: P ( A ∩ B ) = P ( A ) + P ( B ) − P ( A ∪ B ) = P ( A ∣ B ) P ( B ) {\displaystyle P(A\cap B)=P(A)+P(B)-P(A\cup B)=P(A\mid B)P(B)} P ( A ∪ B ) = P ( A ) + P ( B ) − P ( A ∣ B ) P ( B ) {\displaystyle P(A\cup B)={P(A)+P(B)-P(A\mid B){P(B)}}} As the probability of a conditional event [ edit ]

Instead of conditioning on X being exactly x, we could condition on it being closer than distance ϵ {\displaystyle \epsilon } away from x. The event B = { x − ϵ < X < x + ϵ } {\displaystyle B=\{x-\epsilon

a b c d Charles A. Harper (2006). Handbook of plastics technologies: the complete guide to properties and performance. McGraw-Hill Professional. p.17. ISBN 978-0-07-146068-2. Whiteley, Kenneth S.; Heggs, T. Geoffrey; Koch, Hartmut; Mawer, Ralph L.; Immel, Wolfgang (2000). "Polyolefins". Ullmann's Encyclopedia of Industrial Chemistry. Weinheim: Wiley-VCH. doi: 10.1002/14356007.a21_487. Polybutylene ( polybutene-1, poly(1-butene), PB-1) is a polyolefin or saturated polymer with the chemical formula (CH 2CH(Et)) n. Not be confused with polybutene, PB-1 is mainly used in piping. [2] Production [ edit ] Hwo, Charles C.; Watkins, Larry K. Laminated film with improved tear strength, European Patent Application EP0459742, Publication date 12/04/1991

which meets the Kolmogorov definition of conditional probability. [9] Conditioning on an event of probability zero [ edit ] Information for owners of new homes with polybutylene plumbing pipes" (PDF). commerce.wa.gov.au. March 21, 2023. Archived (PDF) from the original on 12 November 2023 . Retrieved November 12, 2023. a b c Mark Alger, Mark S. M. Alger (1997). Polymer science dictionary. Springer. p.398. ISBN 978-0-412-60870-4. While conditional probabilities can provide extremely useful information, limited information is often supplied or at hand. Therefore, it can be useful to reverse or convert a conditional probability using Bayes' theorem: P ( A ∣ B ) = P ( B ∣ A ) P ( A ) P ( B ) {\displaystyle P(A\mid B)={{P(B\mid A)P(A)} \over {P(B)}}} . [4] Another option is to display conditional probabilities in a conditional probability table to illuminate the relationship between events.