Box a contains two red cards and one black card, and box b contains one red card and two black cards. an experiment consists of randomly selecting one card from box a and placing the selected card into box b. then, one card is selected from box b. what is the probability that a red card is selected from box b?

5/12

Step-by-step explanation:

Box A: 2 Red

           1 Black

Box B: 1 Red

           2 Black

One card is selected from Box A and placing the selected card into Box B.

One card is selected from Box B.

What is the probability that a red card is selected from Box B?

Two things can occur:

1) Select red from A and B:

2/3 * 2/4 = 1/3

2) Select black from A and red from B:

1/3 * 1/4 = 1/12

As 1) or 2) can occur:

1/3 + 1/12 = 5/12

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

there is no grid

step-by-step explanation: