Atelevision game show has 6 doors, of which the contestant must pick 2. behind 2 of the doors ate expensive cars, and behind the other 4 doors are consolation prizes. the contestant get to keep the items behind the 2 doors she select. determine the probability that the contestant wins both cars.

In this question, there are 4 consolation door and 2 car doors of total 6 doors. That means for the first door the chance to get consolation is 4/6 and car is 2/6. In second door, only 5 remains so the chance to get consolation is either 4/5 (if 1st door car) or 3/5(if 1st door consolation)

Win 1 car condition:  

1. 1st door car, 2nd door consolation = 2/6 * 4/5 =8/30

2. 1st door consolation, 2nd door car= 4/6 * 2/5 = 8/30

8/30+8/30= 16/30

No car condition

1. 1st door consolation, 2nd door consolation= 4/6 * 3/5= 12/30

At least one car condition

1. 1st door car, 2nd door car = 2/6 * 1/5 =2/30

2. 1st door car, 2nd door consolation = 2/6 * 4/5 =8/30

3. 1st door consolation, 2nd door car= 4/6 * 2/5 = 8/30

2/30 + 8/30 + 8/30= 18/30

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

4x and 6y

im not sure though