If A and B are mutually exclusive events with P(A)= 0.70,then P(B):
A)can be any value between 0 and 1
B)can be any value between 0 and 0.70
C)cannot be larger than 0.30
D)Cannot be determined with the information given

Question

Quizplus · Accepted Answer

If A and B are mutually exclusive, then they cannot occur simultaneously. This means that P(A intersection B) = 0.
We know that P(A) = 0.70. Since A and B are mutually exclusive, we can use the addition rule:
P(A or B) = P(A) + P(B) - P(A intersection B)
But we know that P(A intersection B) = 0, so:
P(A or B) = P(A) + P(B)

Since the probability of any event is between 0 and 1, we can also say that:
P(A or B) <= 1

Therefore:
P(A) + P(B) <= 1
0.70 + P(B) <= 1
P(B) <= 0.30

So, P(B) cannot be larger than 0.30. Therefore, the best answer is C.

If a and B Are Mutually Exclusive Events with P(A)=