Question

Natural numbers from $51$ to $150$ are written on $100$ cards. $A$ card is drawn randomly from this set of $100$ cards. What is the probability that the number written on the card drawn will either be a perfect square or a perfect cube?

• A. $\frac{1}{25}$
• B. $\frac{3}{50}$
• C. $\frac{2}{25}$
• D. $\frac{1}{20}$

Answer 1

Answer: (B)

Perfect square numbers from $51$ to $150$ are $64,81,100,121,144$. So, there are $5$ perfect square numbers from $51$ to $150$
Perfect cubes from $51$ to $150$ are $64,125$. So there are $2$ perfect cubes from $51$ to $150$
Let A be the event that number drawn is perfect square and B be the event that number drawn is perfect cube.
$\therefore P\left(A\right)=\frac{5}{100}$ and $P\left(B\right)=\frac{2}{100}$
Also, $P\left(A\cap B\right)=\frac{1}{100}$
Required probability $=P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)$
$=\frac{5}{100}+\frac{2}{100}-\frac{1}{100}$
$=\frac{6}{100}=\frac{3}{50}$