A number is selected at random from the first twenty-five natural numbers. If it is a composite number, then it is divided by `5`. But if it is not a composite number, it is divided by `2`. The probability that there will be no remainder in the division is

Options

A. `(11)/(30)`
B. `0.4`
C. `0.2`
D. none of these

Answer

C

Explanation

`(c )` Let `C=` the event of the selected number being composite,
`E=` the event of there being no remainder.
`P(C )=(n(C ))/(n(S))=(15)/(25)=(3)/(5)`, `P(barC)=(2)/(5)`
`P(E//C)=(4)/(15)`, `P(E//barC)=(1)/(10)`
`P(E)=P(C )*P(E//C)+P(barC)*P(E//barC)`
`=(3)/(5)*(4)/(15)+(2)/(5)*(1)/(10)=(4)/(25)+(1)/(25)=(1)/(5)=0.2`