Events E and F are such that P(not E or not F) = 0.25, State whether E and F are mutually exclusive.
Solution and Explanation
It is given that P (not E or not F) = 0.25
i.e, P(E'UF') = 0.25
\(⇒\)P(E∩F)'=0.25
Now, P(E∩F) =1-P(E∩F)'
\(⇒\) P(E∩F) =1-0.25
\(⇒\) P(E∩F) =0.75≠0
\(⇒\) E∩F\(≠\phi\)
Thus, E and F are not mutually exclusive.
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Concepts Used:
Axiomatic Approach to Probability
The axiomatic probability perspective is a unifying perspective in which the coherent conditions used in theoretical and experimental probability exhibit subjective probability. Kolmogorov's set of rules or axioms is put to all types of probability. They are known as Kolmogorov's 3 axioms by mathematicians. You can use axiomatic probability to calculate the likelihood of an event that is occurring or not occurring.
The 3 axioms are applicable to all other probability perspectives. This viewpoint is defined as the probability of any function from numbers to events that are satisfied by the three axioms listed below:
- The greatest possible probability is one, and the least possible probability is zero.
- A determined event has a probability of one.
- Two mutually exclusive events cannot happen at the same time, but the union of events states that any one of them can.
