The probability that a random permutation in $S_n$ is a derangement is well known to be $\displaystyle\sum\limits_{j=0}^n (-1)^j \frac{1}{j!}$. In this paper, we consider the Conditional probability that the $(k+1)^{st}$ point is fixed, given there are no fixed points in the first $k$ points. We prove that when $n \neq 3$ and $k \neq 1$, this probability is a decreasing function of both $k$ and $n$. Furthermore, it is proved that this Conditional probability is well approximated by $\frac{1}{n} - \frac{k}{n^2(n-1)}$. Similar results are also obtained about the more general Conditional probability that the $(k+1)^{st}$ point is fixed, given that there are exactly $d$ fixed points in the first $k$ points.

This article includes an interaction between Theology and probability. One of the most significant criticisms of Atheistic Naturalism is the Bayesian theorem which argues through probabilities. This argument includes two main ideas: First, the probability of reliability of cognitive faculties 1 (P(R)=1). Second, the reliability of these faculties in a combination of naturalism and evolution (P(R/N&E)) is low or inscrutable. The advocates of Atheistic Naturalism have criticized this argument: 1. The low P(R/N&E) is not a reason to reject R. 2. If defeating of R by evolutionary Naturalism means abandoning the beliefs to anything including evolutionary Naturalism itself, we have a conclusion beyond defeating the R. 3. The existence of sufficient and independent evidence for R, eliminates self-defeating of N&E. To defend this argument against the criticisms, there are some points and additions: 1. The probability value of P(R/N&E) is not merely low but is low or inscrutable. 2. There are some misunderstandings about defeating of R. 3. There isn't sufficient evidence for R, because it's a cognitive agent. The purpose of the paper is to defend the Bayesian theorem against the critiques of evolutionary naturalism in an analytical, complementary, and critical approach.

"Bankruptcy prediction models" are one of the tools used for making a decision about investing in a corporation. The purpose of the research is to present the best "Conditional probability model" with the ability to predict the economic bankruptcy of corporations in Iran.According to the research results, Four-variable probit & logit models have the most predictive power concerning the economic bankruptcy of corporations in Iran with their descriptive variables:Currenl assets/ Currenliabilitie Grossrofit/ sales NeProfit/ CurrenLiabilitiesAlso, the present research indicates that; first, the trend of the economic bankruptcy of corporations in Iran is not a long-term and slow process, rather corporation's go bankrupt as a result of the economic fluctuations and political variables during some financial periods.Second, the high amounts of production cost, payable interest expense and production bureaucratic expense are considered as the most important intra-organization factors causing the economic bankruptcy of corporations in Iran. Third, profitability variables and variables of covering the liabilities by corporation profit have the most effect in preventing the economic bankruptcy of corporations in Iran.

Massive movements, especially landslides, are one of the most important natural disasters. Landslides endanger people's lives with environmental degradation, their resources and assets. Existence of factors such as prerequisites for roughness, uncontrolled exploitation of forests, non-observance of technical principles for the construction and maintenance of forest and rural roads, lack of proper management and unConditional exploitation of existing resources have exacerbated it. Landslides cause significant damage financially and morally compared to natural hazards such as volcanoes and floods (GOSTI 2005: 408). The landslide every year causes many deaths and injuries in many parts of the world (Abedini et al., 2013), which necessitates the attention to this dangerous phenomenon. The research area in the area of about 9000 square kilometers of the Azerbaijani desert along the east and west to the north of the Aras and the west of the valley of Diz and its east is Qarshou and in the south of Ahar, and from Kasba to the Dare Dize valley along the northwestern slopes of the southern Karnatagh is.

Soils are the outermost layer of the earth's crust, and they are closely interrelated with the formation of the land on which they are formed and developed. Therefore, any change in the geomorphic processes affects the soil-forming processes. "Soil geomorphology" is an assessment of the genetic relationships between soils and landforms. Although the relationships between landforms and soils have been investigated by researchers, a quantitative evaluation of the relationship between soil and geomorphic surface has been less considered. However, the soil-geomorphology relationship is a two-way relationship, and a question arises here is that how an observed soil can indicate geomorphic surfaces or landforms? Accordingly, the current research tries to examine this issue with the use of statistics and Conditional probability. For this purpose, the geomorphic units of the central region of Isfahan were delineated using geopedology approach (Zinck method) and 344 soil profiles were analyzed, and the Conditional probability of the existence of each geomorphic unit was obtained on condition of observation of different soils. The findings quantitatively showed that there is a strong and close relationship between soil development and formation and the geomorphic condition, so that some soils can be found only in certain geomorphic unit. In other words, the soil is an indicator/unique soil for the geomorphic unit. Due to the similar relationship between the geomorphical levels and the soil taxonomical levels, the diversity increased as the taxonomical levels increased from orders to the families. Also, the findings showed slightly in the study area that the effect of "landforms and topography" on the development and formation of soils is more than parent material...

By laying down the principles of probabilities arithmetic, Mohammad Baqir Sadr tried to offer a new reading of argument from design to be efficient for proving the Necessary. The concept of probability has particular complexities and dual meaning from its very initial proposition (statistical probability and epistemological probability). This duality caused different interpretation of probabilities arithmetic. Based on his own basic principles and by using such concepts as non-detailed knowledge and subjective certainty, Sadr regarded the probability the degree of rational belief which is based on external evidence. Having differentiated between Conditional and independent probabilities, he scientifically-inductively arranged the hypothesis of believing in God. Thinkers, especially some contemporary Muslim thinkers, criticized the application of probabilities arithmetic in the argument from design. Some thinkers essentially disagreed with the empirical nature of this argumentation and others permitted the application of probabilities arithmetic not only in proving the existence of God but also in the scope of conceptual intellect by referring to the principle of non-difference and sameness of members of a probable set, but reject it as making certainty. Having reviewed the concept of "probability" and its different interpretations, the present paper seeks to provide a criterion for selecting a proper definition. Then it exposes Sadr' s argument and tries to find appropriate answers for criticisms and doubts cast on this kind of argumentation.

Industries' increasing progress and complexity has made maintenance and repair tasks very challenging, complex, and time-consuming. Maintenance is one of the important sectors in several industries, and improvement in this sector can have excellent results. This paper develops a new maintenance prediction model based on Bayesian networks (BN) capabilities. The models include several variables that experts determine and their influence on each other's-called Conditional probability tables-which are learned from historical data. The model is implemented in an automobile repair department case study to show its performance. The model is evaluated through a sensitivity analysis, and the results show the proficiency of the proposal mode.

Background & Aims: Different scoring systems are used in order to assess the functional quality of intensive care units (ICU) and to predict the required costs and facilities of intensive cares. Variety of scoring systems has been explained that each has advantages and disadvantages. In this study Simplified Acute Physiology Score-III (SAPS-III) and Mortality probability Model-III (MPM-III) were compared. Materials & Methods: The current cross-sectional study was conducted on 240 non-traumatic patients admitted at ICU of Al-Zahra Hospital in 2016-17. Patients' information including demographics, mean of systolic, diastolic and arterial pressure, pulse rate, respiratory rate, temperature, Glasgow Coma Scale(GCS), WBC, hematocrit, bilirubin, creatinine, arterial blood gas, and the presence of underlying diseases was gathered from the records for measurement of MPM-III and SAPS-III scores and then they were compared. Results: This study was conducted on 240 non-traumatic patients. Discrimination of MPM-III in cutoff point of 0. 17 was 0. 83(P<0. 001; 95%CI: 0. 765-0. 898), sensitivity and specificity of this test in prediction of non-traumatic mortality was 82% and 73%, respectively. Discrimination of SAPS-III in cut-off of 48. 5 was 0. 78(P<0. 001; 95%CI: 0. 72-0. 84), while its sensitivity and specificity was 83% and 70%, respectively. Duration of ICU hospitalization (P=0. 028 and 0. 002) and duration of intubation (P=0. 001 and <0. 001) had direct association with mortality based on both scoring systems while total duration of hospitalization was only significant in SAPSIII (P=0. 002). Conclusion: Comparison of SAPS-III and MPM-III in non-traumatic patients presented a higher discrimination ability for MPM-III. In addition, findings showed that mortality in MPM-III was in association with duration of ICU admission and intubation while for SAPS-III, in addition to previous factors, total duration of hospitalization was associated as well.