Question

Given that P(A)=0.7,P(B)= and P (A and B)=0.35

Answer 1

Given $P(A)=0.7, P(B)=0.6,$ and $P(A\cap B)=0.35.$

A.

$$P(B\cap A')=P(B)-P(A\cap B)$$

$$=0.6-0.35=0.25$$

B.

$$P(B')=1-P(B)$$

$$=1-0.6=0.4$$

C.

$$P(A)P(B)=0.7(0.6)=0.42\not=0.35=P(A\cap B)$$

Therefore $A$ and $B$ are dependent events.

D.

$$P(A\cup B)=P(A)+P(B)-P(A\cap B)$$

$$=0.7+0.6-0.35=0.95$$

E.

$$P(B|A)=\dfrac{P(A\cap B)}{P(A)}$$

$$=\dfrac{0.35}{0.7}=0.5$$

F.

$$P(A\cap B)=0.35\not=0$$

Therefore $A$ and $B$ are not mutually exclusive dependent events. e