Question

Analyze the table below and answer the question that follows.

Which of the following can be determined from the table above?

Answer 1

C. Events E and A are independent

Explanation:

we will verify each options

(a)

We can use independent events formula

P(B∩C)=P(B)*P(C)

we are given

P(B)=0.4

P(C)=0.25

P(B∩C)=0.05

now, we can plug these values into formula

and we get

0.05=0.4*0.25

0.05=0.1

we can see that left side is not equal to right side

so, this is FALSE

(b)

We can use independent events formula

P(D∩A)=P(D)*P(A)

we are given

P(D)=0.25

P(A)=0.6

P(D∩A)=0.1

now, we can plug these values into formula

and we get

0.1=0.25*0.6

0.1=0.15

we can see that left side is not equal to right side

so, this is FALSE

(c)

We can use independent events formula

P(E∩A)=P(E)*P(A)

we are given

P(E)=0.5

P(A)=0.6

P(E∩A)=0.3

now, we can plug these values into formula

and we get

0.3=0.5*0.6

0.3=0.3

we can see that both sides are equal

so, this is TRUE

(d)

We can use independent events formula

P(D∩B)=P(D)*P(B)

we are given

P(D)=0.25

P(B)=0.4

P(D∩A)=0.15

now, we can plug these values into formula

and we get

0.15=0.25*0.4

0.15=0.1

we can see that left side is not equal to right side

so, this is FALSE