What is Probability? Probability is the measure of that how many times an event can happen, Now we know the definition of probability but the definition only is not enough to know the probability of happening at least one event, So we need theories and rules to find the probability of happening event, Theories that solve probability’s problems which are several types, For example if we have two events are mutual then there’s a probability of at least one of the events happens according to:P(AUB)=1.As “B&A” are the names of the events Another equation for this problem is:P(A) + P(B)- P(A?B). n(AUB) = n(A) + n(B)- n(A?B).We can prove these equations, As we know that the events are sets and the set theory is:n(AUB) = n(A) + n(B)- n(A?B).Divide it by the sample space “S”You get this: n(AUB)/ n(S) = n(A)/ n(S) + n(B)/ n(S)- n(A?B)/ n(S)And according to the probability definition you get this equation:P(AUB) = P(A) + P(B)- P(A?B). #And you can learn more by searching for some examples on the internet, and this is called addition theorem If A and B are any two events of a sample space such that:P(A) ?0 and P(B)?0, thenP(A?B) = P(A) * P(B|A) = P(B) *P(A|B).
For example: If P(A) = 1/5 P(B|A) = 1/3 then what is P(A?B)?Solution: P(A?B) = P(A) * P(B|A) = 1/5 * 1/3 = 1/15And this is called multiplication theorem.Also there are a lot of types of theories that I didnot mention, Search for more informationNow that I am going to talk about the types of variables in statistics and probability specially:Types of variables are 8 types which are:1. Independent.2. Dependent.3a. Controlled.3b.
Quantitative.6. Discrete.7. Continuous.8. Random and Binomial.First we are going to talk about: independent typeThe independent variable is the variable that you can change it yourselfSecond type is dependent type which you cannot change it, or have control on itThe third type is not actually a type but another name of the first typeThe fourth type is control and this type is a constant that help you with two other variables