Question

If A and B are mutually exclusive events $P\left(A\right)=\frac{3}{8}\text{and}P\left(B\right)=\frac{1}{8},\text{then find}P(A^{\prime }\cup B^{\prime }).$

• A. 1
• B. 0.0
• C. 0.8
• D. 0.5

Answer 1

The correct option is A 1

$\text{Given:}\left(P\right(A)=\frac{3}{8}P(B)=\frac{1}{8}$

Since A and B are mutually exclusive events, $P(A\cap B)=0.$

$P(A^{\prime }\cup B^{\prime })=P(A\cap B{)}^{\prime }P(A\cap B{)}^{\prime }=1-P(A\cap B)=1-0P(A\cap B{)}^{\prime }=1$
So, $P(A^{\prime }\cup B^{\prime })=1.$