SOLUTION: Events A and B are mutually exclusive. Suppose P(A)=0.21 and P(B)=0.05. What is the probability that neither A nor B will occur? Use two decimal digits.

Question 1095341: Events A and B are mutually exclusive. Suppose P(A)=0.21 and P(B)=0.05.
What is the probability that neither A nor B will occur?
Use two decimal digits.

Answer by Edwin McCravy(20060) (Show Source): You can put this solution on YOUR website!

The probability that neither occur is the complement of the
event that A or B occurs. 

So we will first calculate P(A or B)

P(A or B) = P(A) + P(B) - P(A and B)

But since they are mutually exclusive, P(A and B) = 0

P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = P(A) + P(B) - 0
P(A or B) = P(A) + P(B)
P(A or B) = 0.21 + 0.05
P(A or B) = 0.26

The complement of the event (A or B) has probability

1 - 0.26 = 0.74

Edwin

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