Let A and B be mutually exclusive events. Which of the following is always TRUE for these events?Group of answer choicesP(A and B) = P(A) x P(B)P(A or B) = P(A) + P(B)P(A or B) = P(A) + P(B) - P(A) x P(B)all of the above are always true
Question
Let A and B be mutually exclusive events. Which of the following is always TRUE for these events?Group of answer choicesP(A and B) = P(A) x P(B)P(A or B) = P(A) + P(B)P(A or B) = P(A) + P(B) - P(A) x P(B)all of the above are always true
Solution
The correct answer is "P(A or B) = P(A) + P(B)".
This is because A and B are mutually exclusive events, which means they cannot occur at the same time. Therefore, the probability of either A or B occurring is simply the sum of their individual probabilities.
The other options are not always true for mutually exclusive events. For example, "P(A and B) = P(A) x P(B)" is true for independent events, not mutually exclusive events. Similarly, "P(A or B) = P(A) + P(B) - P(A) x P(B)" is the formula for the union of two events that are not mutually exclusive.
So, the only statement that is always true for mutually exclusive events is "P(A or B) = P(A) + P(B)".
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