Question

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 division is

• A. $\frac{11}{30}$
• B. $.0.4$
• C. $0.2$
• D. none of these

Answer 1

Answer: (C)

$0.2$

$First25naturalnumbersare1,2,3,.............,24,25Noofwaysanumbercanbeselected=\left(\begin{array}{c}25\\ 1\end{array}\right)compositenumberswhicharedivisibleby5=10,15,20,25andnon-compositewhicharedivisibleby2=2\therefore Totalnumberoffavourableoutcome=\left(\begin{array}{c}5\\ 1\end{array}\right)LetEbetheeventthattheselectednumberiscompletelydivisible\Rightarrow P\left(E\right)=\frac{\left(\begin{array}{c}5\\ 1\end{array}\right)}{\left(\begin{array}{c}25\\ 1\end{array}\right)}=\frac{1}{5}=0.2$