osaad said:i need a general form to solve Prob(a or b or c ... or z) that r not mutually exclusive.
i managed to derive it for 2,3 and 4 variables but i can't seem to get a general form out of it, its recursive.
any1 know a way?
awkward said:It's called the Principle of Inclusion / Exclusion.
http://en.wikipedia.org/wiki/Principle_of_inclusion-exclusion#In_probability
When events are not mutually exclusive, it means that they can occur at the same time. In other words, the occurrence of one event does not prevent the occurrence of another event.
To calculate the probability of "a or b or c or z" when the events are not mutually exclusive, you can use the formula P(a or b or c or z) = P(a) + P(b) + P(c) + P(z) - P(a and b) - P(a and c) - P(a and z) - P(b and c) - P(b and z) - P(c and z) + P(a and b and c) + P(a and b and z) + P(a and c and z) + P(b and c and z) - P(a and b and c and z). This formula takes into account the overlap between the events.
No, the probability of "a or b or c or z" cannot be greater than 1 even if the events are not mutually exclusive. The total probability of all possible outcomes must always equal 1.
When the events are not mutually exclusive, the probability of "a or b or c or z" will increase because there are more ways for the event to occur. This is because the overlap between the events allows for multiple ways for the event to happen.
Yes, "a or b or c or z" can be independent events even if they are not mutually exclusive. This is because independence means that the occurrence of one event does not affect the probability of the other event happening. In this case, while the events may overlap, the probability of one event occurring does not impact the probability of another event occurring.