A number is selected at random from the first 25 natural numbers. If it is a composite number, then it is divided by 6. But if it is not a composite number, it is divided by 2. Find the probability that there will be no remainder in the division.

Answer

`0.2`

Explanation

Lec C be the event of the selected number being composite and E be 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).`
`=3/5xx4/15+2/5xx1/10=4/25+1/25=1/5=0.2`