Question

cards numbered 1 to 30 are put in a, bag . a card is drawn at random . find the probability that the card is
1. not a perfect square

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{S}\mathrm{be}\mathrm{the}\mathrm{sample}\mathrm{space}. \\ \mathrm{S}=\left\{1,2,3,4,............,29,30\right\} \\ \mathrm{n}\left(\mathrm{S}\right)=30 \\ \mathrm{Let}\mathrm{E}\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{card}\mathrm{bearing}\mathrm{a}\mathrm{perfect}\mathrm{square}\mathrm{number}. \\ \mathrm{E}=\left\{1,4,9,16,25\right\} \\ \mathrm{n}\left(\mathrm{E}\right)=5 \\ \mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{n}\left(\mathrm{E}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{5}{30}=\frac{1}{6} \\ \mathrm{Now},\mathrm{P}\left(\mathrm{getting}\mathrm{non}\mathrm{perfect}\mathrm{square}\right)=\mathrm{P}\left(\overline{\mathrm{E}}\right)=1-\mathrm{P}\left(\mathrm{E}\right)=1-\frac{1}{6}=\frac{5}{6} \end{gathered}$$