Question

Cards bearing numbers from 13-60 are placed in a box and mixed throughly. One card is drawn at random. Find the probability that the number on the card is
i) divisible by 5 ii) a perfect square

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{S}\mathrm{be}\mathrm{the}\mathrm{sample}\mathrm{space}. \\ \mathrm{S}=\left\{13,14,15,......60\right\} \\ \mathrm{n}\left(\mathrm{S}\right)=48. \\ \left(1\right). \\ \mathrm{Let}\mathrm{E}\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{card}\mathrm{bearing}\mathrm{a}\mathrm{number}\mathrm{divisible}\mathrm{by}5. \\ \mathrm{E}=\left\{15,20,25,30,35,40,45,50,55,60\right\} \\ \mathrm{n}\left(\mathrm{E}\right)=10 \\ \mathrm{p}\left(\mathrm{E}\right)=\frac{\mathrm{n}\left(\mathrm{E}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{10}{48}=\frac{5}{24} \\ \left(2\right) \\ \mathrm{Let}\mathrm{F}\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{card}\mathrm{bearing}\mathrm{a}\mathrm{number}\mathrm{that}\mathrm{is}\mathrm{a}\mathrm{perfect}\mathrm{square}. \\ \mathrm{F}=\left\{16,25,36,49\right\} \\ \mathrm{n}\left(\mathrm{F}\right)=4 \\ \mathrm{now},\mathrm{p}\left(\mathrm{F}\right)=\frac{\mathrm{n}\left(\mathrm{F}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{4}{48}=\frac{1}{12} \end{gathered}$$