Which of the following can be determined about events a and c from the table.

a. p(a | c) = 0.16, p(a) = 0.16, the events are independent

b. p(a | c) = 0.16, p(c) = 0.16, the events are independent

c. p(c | a) = 0.75, p(c)=0.75 the events are not independent

d. p(c | a) = 0.75, p(a)=0.75 the events are not independent

Option: A is the correct answer.

       A. P(A | C) = 0.16, P(A) = 0.16, the events are independent

Step-by-step explanation:

We know that two events A and B are said to be independent if:

(

Since, we know that if A and B are two independent events then

and:

and hence using property (1) we get:

  )

from the given table we have:

and also, P(A)=0.16

As P(A|C)=P(A)

     Hence, events A and C are independent.

Also we may observe that:

(

Since, from table we have:

P(C)=0.75

and

)

Hence, events A and C are independent.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0