Question Number 106305 by bemath last updated on 04/Aug/20
$$\mathrm{what}\:\mathrm{is}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{5}\:\mathrm{coming}\:\mathrm{up}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{if}\:\mathrm{a}\:\mathrm{die}\: \\ $$$$\mathrm{is}\:\mathrm{rolled}\:\mathrm{3}\:\mathrm{times}\: \\ $$
Answered by Ar Brandon last updated on 04/Aug/20
$$\mathrm{P}\left(\mathrm{Atleast}\:\mathrm{one}\:\mathrm{5}\right)=\mathrm{1}−\mathrm{P}\left(\mathrm{No}\:\mathrm{5}\right) \\ $$$$\mathrm{P}\left(\mathrm{No}\:\mathrm{5}\right)=\left(\frac{\mathrm{5}}{\mathrm{6}}\right)^{\mathrm{3}} \\ $$$$\Rightarrow\mathrm{P}\left(\mathrm{Atleast}\:\mathrm{one}\:\mathrm{5}\right)=\mathrm{1}−\left(\frac{\mathrm{5}}{\mathrm{6}}\right)^{\mathrm{3}} \\ $$
Commented by bemath last updated on 04/Aug/20
$$\mathrm{cooll} \\ $$