Question

in a bottle there are 7 red buttons , 5 green buttons and 8 purple buttons. what is the probability that randomly drawn button from the bottl is purple button? if one extra green button is put in the side of the
bottle , what will be the probability that randomly drawn button is purple?

Answer 1

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{red}\mathrm{buttons}=7 \\ \mathrm{Number}\mathrm{of}\mathrm{green}\mathrm{buttons}=5 \\ \mathrm{Number}\mathrm{of}\mathrm{purple}\mathrm{buttons}=8 \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{buttons}=7+5+8=20 \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}=20 \\ \mathrm{Number}\mathrm{of}\mathrm{purple}\mathrm{buttons}=8 \\ \mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}=8 \\ \mathrm{P}\left(\mathrm{a}\mathrm{purple}\mathrm{button}\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}}=\frac{8}{20}=\frac{2}{5} \\ \mathrm{Now},\mathrm{when}\mathrm{one}\mathrm{extra}\mathrm{green}\mathrm{button}\mathrm{is}\mathrm{put}\mathrm{in}\mathrm{the}\mathrm{bottle},\mathrm{then} \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{buttons}\mathrm{in}\mathrm{the}\mathrm{bottle}=20+1=21 \\ \mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}=21 \\ \mathrm{Number}\mathrm{of}\mathrm{purple}\mathrm{buttons}=8 \\ \mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}=8 \\ \mathrm{P}\left(\mathrm{a}\mathrm{purple}\mathrm{button}\right)=\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{possible}\mathrm{outcomes}}=\frac{8}{21} \end{gathered}$$