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The Statistics Online Computational Resource (SOCR) [1] is an online multi-institutional research and education organization. SOCR designs, validates and broadly shares a suite of online tools for statistical computing, and interactive materials for hands-on learning and teaching concepts in data science, statistical analysis and probability theory.
Therefore, some of the hands-on activities might not be based on a multiplicative relation. Here is a picture of two students working with an apparatus where the constant sum relation is correct. It is not always possible or feasible to put carefully designed hands-on activities into the hands of students.
To find the likelihood of a certain point range, one simply subtracts the two relevant cumulative probabilities. So, the likelihood of being dealt a 12-19 HCP hand (ranges inclusive) is the probability of having at most 19 HCP minus the probability of having at most 11 HCP, or: 0.9855 − 0.6518 = 0.3337. [2]
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. [1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one.
SAPHIRE is a probabilistic risk and reliability assessment software tool. SAPHIRE stands for Systems Analysis Programs for Hands-on Integrated Reliability Evaluations.The system was developed for the U.S. Nuclear Regulatory Commission (NRC) by the Idaho National Laboratory.
The Probability of drawing a given hand is calculated by dividing the number of ways of drawing the hand (Frequency) by the total number of 5-card hands (the sample space; () =,,). For example, there are 4 different ways to draw a royal flush (one for each suit), so the probability is 4 / 2,598,960 , or one in 649,740.
The SOCR resource pages contain a number of hands-on interactive activities and demonstrations of random number generation using Java applets. The Quantum Optics Group at the ANU generates random numbers sourced from quantum vacuum. Samples of random numbers are available at their quantum random number generator research page.
The probability for winning will be much higher than 50%, depending on the number of players in the puzzle configuration: for example, a winning probability of 87.5% for 7 players. Similar strategies can be applied to team sizes of N = 2 k −1 and achieve a win rate (2 k-1)/2 k.