We choose a number from the set {1, 2, 3, . . . , 100}, uniformly at random. Let X be the chosen number. For each of the following choices determine if the two events are independent or not. Explain why. (a) A = {X is even), B = (X is divisible by 5}
(b) C = (X has two digits), D = {X is divisible by 3}
(c) E = {X, is a prime}, F = has a digit 5 prime number

(a) A and B are not independent.

(B) C and D are not independent.

(C) E and F are not independent.

Step-by-step explanation:

Two events are called independent If the output sets for the two events do not have any common element.

i.e. their intersection is Null.

If P and Q are independent events then

Now, let us have a look at the given questions and find whether they are independent or not as per above definition

(a) A = {X is even}, B = {X is divisible by 5}

A = {2, 4, 6, 8, 10, .....20, 22, 24, ..... }

B = {5, 10, 15, 20,  ....}

A and B have common elements {10, 20, 30, ....}

So, the two events are not independent.

(b) C = {X has two digits}, D = {X is divisible by 3}

C = {11, 12, 13, ......, 99}

D = {3, 6, 9 12, 15, .... , 99}

C and D have common elements {3, 6, 9 12, 15, .... , 99}

So, the two events are not independent.

(c) E = {X, is a prime}, F = has a digit 5 prime number

E = {2, 3, 5, 7, 11, 13, 17, 19, 23, .....}

F = {5}

E and F have common element {5}

So, the two events are not independent.

So, the answer are:

(a) A and B are not independent.

(B) C and D are not independent.

(C) E and F are not independent.

i think it might be a but you might want a second opinion

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!