Respuesta :
Answer:
(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.
[tex]P(E|F)=\frac{P(E\bigcap F)}{P(F)}[/tex]
(a)
From the conditional probability we get:
[tex]P(E|F)=\frac{P(E\bigcap F)}{P(F)}[/tex]
[tex]\Rightarrow 0.07 =\frac{0.021}{P(F)}[/tex] [ putting the value of P(E|F) and P(E∩F)]
[tex]\Rightarrow P(F) \times 0.07=0.021[/tex]
[tex]\Rightarrow P(F) =\frac{0.021}{0.07}[/tex]
⇒P(F)=0.3
(b)
similarly,
[tex]P(F|E)=\frac{P(E\bigcap F)}{P(E)}[/tex]
[tex]\Rightarrow 0.1=\frac{0.021}{P(E)}[/tex]
[tex]\Rightarrow P(E) \times 0.1= 0.021[/tex]
[tex]\Rightarrow P(E) =\frac{ 0.021}{0.1}[/tex]
⇒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.
