Question

30) Cards with numbers 2 to 101 are placed in a box. Find the probability that the card which is selected has a number which is perfect square.

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{S}\mathrm{be}\mathrm{the}\mathrm{sample}\mathrm{space}. \\ \mathrm{S}=\left\{2,3,4,5,........101\right\} \\ \mathrm{n}\left(\mathrm{S}\right)=100 \\ \mathrm{Let}\mathrm{E}\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{card}\mathrm{bearing}\mathrm{a}\mathrm{perfect}\mathrm{square}\mathrm{number}. \\ \mathrm{E}=\left\{4,9,16,25,36,49,64,81,100\right\} \\ \mathrm{n}\left(\mathrm{E}\right)=9 \\ \mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{n}\left(\mathrm{E}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{9}{100} \end{gathered}$$