Question

A two digit number is to be formed from the digits 0, 1, 2, 3, 4. Repetition of the digits is allowed. Find the probability that the number so formed is a: 

i. prime number. 

ii. multiple of 4. 

iii multiple of 11.

Answer 1

Sample space

(S) = {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

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

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

∴ C = {11, 22, 33, 44}

∴ n(C) = 4