Suppose that an experiment has five separate mutually exclusive outcomes: A, B, C, D, and E. If the sample space for the experiment is a uniform sample space, what is P (A, B or E)?
P(A∪B∪E)
=P(A)+P(B)+P(E)
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Note that the probabilities can be added only if the events are mutually exclusive, as specified in the question.
To find the probability of event A, B, or E occurring, we need to sum up the individual probabilities of each event and add them together.
In this case, we have five mutually exclusive outcomes - A, B, C, D, and E. If the sample space is uniform, it means that each outcome has an equal probability of occurring.
Since we are interested in the probability of A, B, or E, we need to calculate the probability of each event separately and then add them up.
Let's assume that each event has a probability of P(A), P(B), P(C), P(D), and P(E), respectively.
Since the outcomes are mutually exclusive, the sum of the probabilities of all events must be equal to 1:
P(A) + P(B) + P(C) + P(D) + P(E) = 1
If the sample space is uniform, then each outcome has an equal probability, which means:
P(A) = P(B) = P(C) = P(D) = P(E)
Let's call this common probability as p:
P(A) = P(B) = P(C) = P(D) = P(E) = p
Now, we can write the equation as:
p + p + p + p + p = 1
5p = 1
Solving for p:
p = 1/5
Now, we can substitute this value back into the equation to find the probability of A, B, or E:
P(A, B or E) = P(A) + P(B) + P(E) = p + p + p = 3p
Substituting p = 1/5:
P(A, B or E) = 3 * (1/5) = 3/5
Therefore, the probability of either event A, B, or E occurring is 3/5.