Question

the coin is tossed twice what is the probability at most 2 heads occur,what is the probability at least 1 head occur ?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{S}\mathrm{be}\mathrm{the}\mathrm{sample}\mathrm{space}. \\ \mathrm{S}=\left\{\mathrm{HH},\mathrm{HT},\mathrm{TH},\mathrm{TT}\right\} \\ \mathrm{n}\left(\mathrm{S}\right)=4 \\ \mathrm{Let}\mathrm{E}\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{at}\mathrm{most}2\mathrm{heads}. \\ \mathrm{E}=\left\{\mathrm{HH},\mathrm{HT},\mathrm{TH},\mathrm{TT}\right\} \\ \mathrm{n}\left(\mathrm{E}\right)=4 \\ \mathrm{P}\left(\mathrm{E}\right)=\frac{\mathrm{n}\left(\mathrm{E}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{4}{4}=1 \\ \mathrm{Let}\mathrm{F}\mathrm{be}\mathrm{the}\mathrm{event}\mathrm{of}\mathrm{getting}\mathrm{at}\mathrm{least}1\mathrm{head}. \\ \mathrm{F}=\left\{\mathrm{HT},\mathrm{TH},\mathrm{HH}\right\} \\ \mathrm{n}\left(\mathrm{F}\right)=3 \\ \mathrm{P}\left(\mathrm{F}\right)=\frac{\mathrm{n}\left(\mathrm{F}\right)}{\mathrm{n}\left(\mathrm{S}\right)}=\frac{3}{4} \end{gathered}$$