Question

a coin is tossed 12 times. what is the probability of getting exactly
10 tails

Answer 1

$$\begin{gathered} \mathrm{Assuming}\mathrm{that}\mathrm{the}\mathrm{coin}\mathrm{is}\mathrm{unbiased},\mathrm{the}\mathrm{probability}\mathrm{of}\mathrm{all}\mathrm{type}\mathrm{of}\mathrm{events}\mathrm{would}\mathrm{be}\mathrm{same}\mathrm{as}\mathrm{probability}\mathrm{of}\mathrm{head}\mathrm{and}\mathrm{tale}\mathrm{is}\mathrm{same}. \\ \mathrm{Therefore},\mathrm{probability}\mathrm{of}\mathrm{getting}\mathrm{exactly}10\mathrm{tails}\left(\mathrm{P}\right)=\frac{\mathrm{number}\mathrm{of}\mathrm{ways}10\mathrm{tails}\mathrm{come}}{\mathrm{total}\mathrm{possible}\mathrm{events}} \\ \mathrm{So},\mathrm{P}=\frac{{}^{12}\mathrm{C}_{10}}{2^{12}}=\frac{33}{2048} \end{gathered}$$