An experiment consists of rolling a standard six-sided die once. Event A is "rolling an even number" and event B is "rolling a 2."

Are the events dependent or independent? Why?

Select the option that correctly answers both questions.

Events A and B are independent, because P(B)=P(B|A)=1/6.

Events A and B are dependent, because P(A)≠P(B|A).

Events A and B are independent, because P(A)=P(B|A)=1/2.

Events A and B are dependent, because P(B)≠P(B|A).

(D)Events A and B are dependent, because P(B)≠P(B|A).

Step-by-step explanation:

Definition: Two events are independent if

An experiment consists of rolling a standard six-sided die once.

Event A is "rolling an even number"

Even numbers are 2,4 and 6

Event B is "rolling a 2."

Substitution into

Left Hand Side =1/6

Right Hand Side =(1/6)÷(1/2)=1/3

Since , therefore which makes the events dependent.

y=x+2 hope this jdjxhdnzbdjdo

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12