Let the sample space be Upper S equals StartSet 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 comma 10 EndSet. Suppose the outcomes are equally likely. Compute the probability of the event Upper E equals StartSet 1 comma 4 comma 7 comma 9 EndSet.

Probability of event E = (4/10) = 0.40

Step-by-step explanation:

Note that n(E) is the number of outcomes in E

n(S) is the number of outcomes in S

And with each outcome having equal likelihood of occurring,

SetS = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

n(S) = 10

Event E = {1, 4, 7, 9}.

n(E) = 4

Probability of event E = n(E)/n(S)

Probability of event E = (4/10) = 0.40

Hope this Helps!!

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

where is the option given