Answer to Question #128080 in Statistics and Probability for ysabe castro

Question

Given P(E) = 0.25, P(F) = 0.6, and P(E ∪ F) = 0.7.
Find:

Answer 1

$$P(E\cup F)=P(E)+P(F)-P(E\cap F)$$

$$P(E\cap F)=P(E)+P(F)-P(E\cup F)=$$

$$=0.25+0.6-0.7=0.15$$

Since $P(E\cap F)\not =0,$ then event $E$ and event $F$ are not mutually exclusive.

$$P(E)\cdot P(F)=0.25\cdot0.6=0.15=P(E\cap F)$$

Event $E$ and event $F$ are independent.