1.

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»

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 

∴ P(A) = \(\frac{n(A)}{n(S)}\) = 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 

∴ P(B) = \(\frac{n(B)}{n(S)}\) = 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

∴ P(C) = \(\frac{n(C)}{n(S)}\) = 4/20

∴ P(C) = 1/5

∴ P(A) = 3/10, P(B) = 3/10, P(C) = 1/5


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