Consider the two events A and B. The probability that at least one of A or B occurs is 0· 6. If the probability of both A and B occurring is 0· 3, then…

P(A∪ B)=P(A)+P(B)-P(A∩ B), so P(A)+P(B)=0.6+0.3=0.9 P(A')+P(B')=2-[P(A)+P(B)]=2-0.9 1.1

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Solve the following.

Consider the two events A and B. The probability that at least one of A or B occurs is 0· 6. If the…

Consider the two events $A$ and $B$. The probability that at least one of $A$ or $B$ occurs is $0\cdot 6$. If the probability of both $A$ and $B$ occurring is $0\cdot 3$, then calculate $P(A') + P(B')$.

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Answer

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$, so $P(A)+P(B)=0.6+0.3=0.9$ $P(A')+P(B')=2-[P(A)+P(B)]=2-0.9$

Final answer: 1.1