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If we needed to assign probabilities to each outcome, we could roll the die several times and see the frequency of the values. Theoretically, we should see each face come up with the same frequency and then assign the probabilities based on them. com 33 A Handbook of Statistics Probability There are two important rules to be mindful of when assigning probabilities to simple events. These rules are stated below. The Rules of Probability Rule #1: All simple event probabilities must be between 0 and 1.

Mathematically, it is calculated as the weighted average of each possible value. The weights are the probability of the event occurring. Like the means we looked at in chapter 2, it is a measurement for where the distribution is centered. The expected value is not necessarily the event with the highest probability and since we are taking a weighted average, the expected value is not necessarily one of the outcomes of the experiment. com 45 A Handbook of Statistics Random Variables and Probability Distributions The formula for calculating the expected value for a discrete random variable x, denoted by µ, is µ=∑xp(x) The variance of a discrete random variable x, denoted by σ2 is σ2=E[(x- µ)2]= ∑(x-µ)2p(x) The standard deviation is the square root of the variance.

Written using formulas: P(A|B)=P(A) P(B|A)=P(B) The benefit to having independent events is that it makes the calculation of the intersection rule much easier – All you have to do is multiply the two events together. 5 Probability Chapter 4 Problems 1) An experiment results in one of the following sample points: E1, E2, E3, E4, or E5. 1 2) The sample space for an experiment contains five sample points with probabilities as shown in the table below. 15 Find the probabilities of A: {Either 1, 2, or 3 occurs}.

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