Comment on the three types of probability

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Can you post an example of two events that are not mutually exclusive as well as not collectively exhaustive? What is the probability of getting a 3 or 5 in a throw of a six-faced die? Can you also comment on the three types of probability?

Two events are said to be not mutually exclusive when there is a possibility at least any one of the two events occur at the same time. An event is said to be collectively exhaustive when there is a chance that at least one of the events will occur. The example for not mutually exclusive and not collective exhaustive events is “rolling a die and getting either a prime number or even number”. Another example of not mutually exclusive as well as not collectively exhaustive events are “rolling a die and getting a number divisible by both 2 and 3”

Two events are said to be mutually exclusive if the occurrence of one event affects the occurrence of other events. Normally the probability value is positive and it falls between 0 and 1. The sum of the probability of all possible events equals to 1. In addition, the probability value can be expressed either in percentages, fractions or decimals

In rolling a single faced die, the sample space is

S = (1, 2, 3, 4, 5, 6)

Let A be the event of getting 3

Let B be the event of getting 5

P (A) = 1/6

P (B) = 1/6

P (A and B) = 0

P (A or B) = 1/6 + 1/6 = 2/6 = 1/3

Thus, we see that the probability of getting either 3 or 5 1/3

The three types of probability are 

Theoretical Probability approach

Relative Probability approach, and

Subjective Probability approach

For theoretical probability, there is equal likely chance for any event to occur with probability 1/n

For relative probability, the probability is computed using the frequency of an observation or an actual measurement

For subjective probability, the values are calculated which was taken between any range. For example, the probability of choosing a day from the month is 1/30

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