A two digit number is to be formed from the digits 0,1,2,3,4 Repetition of the is allowed. find the probability that the number so formed is a-- a) prime number.
b) multiple of 4
c)multiple of 11​

Sample space = {10, 11, 12, 13, 14, 20, 21, 22, 23, 24, 30, 31, 32, 33, 34, 40, 41, 42, 43, 44}

∴ n(S) = 20 .

[i] Let A be the event that the number so formed is a prime number.

∴ A = {11,13,23,31,41,43}

∴ n(A) = 6

So, P(A) = n(A)/n(S) = 6/20

∴ P(A) = 3/10.

[ii] Let B be the event that the number so formed is a multiple of 4.

∴ B = {12,20,24,32,40,44}

∴ n(B) = 6

So, P(B) = n(B)/n(S) = 6/20

∴ P(B) = 3/10.

[iii] Let C be the event that the number so formed is a multiple of 11.

∴ C = {11,22,33,44}

∴ n(C) = 4

So, P(C) = n(C)/n(S) = 4/20

∴ P(C) = 1/5.

Numbers are:

10,11,12,13,14,20,21,22,23,24,30,31,32,33,34,40,41,42,43,44

1) Prime number

11,13,23,29,31,37,41,43

P = 8/20.

2)Multiple of 4

12,16,20,24,28,32,36,40,44

P = 9/20.

3)Multiple of 11

11,22,33,44

P = 4/20.

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

this is a very good question

step-by-step explanation:

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