Question

The probability that at least one of A and B occurs is $0.6$. If A and B occur simultaneously with probability $0.3$, then $P\left(A^{\prime }\right)+P\left(B^{\prime }\right)$ is

• A. $0.9$
• B. $0.15$
• C. $1.1$
• D. $1.2$

Answer 1

The correct option is C $1.1$

$ProbabilityofeventAbep\left(A\right)andthatofeventbep\left(B\right)ProbabilitythatatleastoneofAandBoccurs=1-probabilitythatneitherAnorBoccurs0.6=1-p\left(A^{\prime }\right)\ast p\left(B^{\prime }\right)\Rightarrow p\left(A^{\prime }\right)\ast p\left(B^{\prime }\right)=0.4ProbabilityofAandBoccurssimultaneously=p\left(A\right)\ast p\left(B\right)=(1-p(A^{\prime }\left)\right)\ast (1-p(B^{\prime }\left)\right)\Rightarrow 0.3=1-p\left(A^{\prime }\right)-p\left(B^{\prime }\right)+p\left(A^{\prime }\right)\ast p\left(B^{\prime }\right)\Rightarrow p\left(A^{\prime }\right)+p\left(B^{\prime }\right)=0.7+p\left(A^{\prime }\right)\ast p\left(B^{\prime }\right)=0.7+0.4=1.1$