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.

thus, the first answer choice, y = sec x, is the correct one