(1 point) If P(E∩F)=0.021P(E∩F)=0.021, P(E|F)=0.07P(E|F)=0.07, and P(F|E)=0.1P(F|E)=0.1, then

(a) P(E)=P(E)=

(b) P(F)=P(F)=

(c) P(E∪F)=P(E∪F)=

(d) Are the events EE and FF independent? Enter yes or no .

(a)P(F)=0.3

(b)P(E)=0.21

(c) P(E∪F) = 0.489

(d)Therefore E and F are dependent event.

Step-by-step explanation:

Given that ,

P(E∩F) = 0.021  and  P(E|F)= 0.07 and  P(F|E).

Conditional probability: When an event occurring in presences of other event that probability is known as conditional probability.

(a)

From the conditional probability we get:

       [ putting the value of P(E|F) and P(E∩F)]

⇒P(F)=0.3

(b)

similarly,

⇒P(E)= 0.21

(c)

P(A∩B)=0 then event A and B are mutually exclusive.

Then P(A∪B)= P(A)+P(B)

and P(A|B) = 0

Again P(A∩B) ≠ 0 then event A and B are mutually inclusive.

Then P(A∪B) = P(A)+P(B)-P(A∩B)

Since P(E∩F) = 0.021 then event E and F are mutually inclusive.

Therefore P(E∪F) = P(E)+P(F)-P(E∩F)

        ⇒ P(E∪F) =  0.21+0.3-0.021

       ⇒ P(E∪F) = 0.489

(d)

We know that in conditional probability an event occur on occurring of other event.

Independent event: When an event does not affect another event . Then this two event is known as independent event.

But here event E and F both outcomes are affected by each other.

Therefore E and F are dependent event.

the answer is 40.

proof: