A drawer contains 3 red paper clips 5 green paper clips and 4 blue paperclips one paper clip is taken from the drawer then replaced another paper clip is taken from the drawer what is the probability that the first paper clip is red and the second paper clip is blue?

3/12 for red

4/12 for blue

Step-by-step explanation:

3 is red

5 is green

4 is blue

3 + 5 + 4 is 12 so it is out of 12 altogether

3/12 for red

4/12 for blue

1/12

Step-by-step explanation:

To find the probability of the event occuring, we need to find the probabilites of taking a red paperclip and taking a blue paperclip and then multiply them together.

Red paperclip:

3/12 = 1/4

Blue paperclip:

4/12 = 1/3

Probability of event:

3/12 x 4/12 = 12/144 = 1/12

1/4 x 1/3 = 1/12

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