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-
A. (1) prime number.
B. (2) multiple of 4.
C. (3) multiple of 11.
D.

Answer 1

Correct Answer - A::B::C
As we have to form two-digits numbers,
0 cannot be at tens place. The sample space
`S={10,11,12,13,20,21,22,23,24,30,31,32,33,34,40,41,42,43,44}`
`thereforen(S)=20`
Let A be the event that the number formed is a prime number.
Then A `={11,13,23,31,41,43}" "thereforen(A)=6`
`P(A)=(n(A))/(n(S))=(6)/(20)=(3)/(10).`
Let B be the event that the number formed is a multiple of 4.
Then `B={12,20,24,32,40,44}" "thereforen(B)=6.`
`P(B)=(n(B))/(n(S))=(6)/(20)=(3)/(10).`
Let C be the event that the number formed is a multiple of 11.
Then C `={11,22,33,44}" "thereforen(C)=4`
`P(C)=(n(C))/(n(S))=(4)/(20)=(1)/(5).`