91Ó°ÊÓ

Probability is defined as the ratio of the number of microstates in a given microstate to the total number of microstates in a system.

Microstates corresponding to 100 H & 0T = 1

Microstates corresponding to 0 H & 100 T= 1

Total microstates 1.27 × 10³⁰

Time for tossing 100 coins = 1 sec

Time for the event (100 H or 100T) to occur

\begin{aligned}t = \frac{{1.27 \times {{10}^{30}}}}{2}\\= 0.635 \times {10^{30}}\sec onds\end{aligned}

Time in years

\begin{aligned}t = 0.635 \times {10^{30}}\sec onds\\= \frac{{0.635 \times {{10}^{30}}}}{{24 \times 60 \times 60 \times 365}}{\rm{years}}\\= 2.02 \times {10^{22}}\;{\rm{years}} \end{aligned}

Therefore, the notion is verified that if we toss 100 coins each second, we expect 100 heads or 100 tails once in 2×10²². The time in 2-digit accuracy is 2.02 ×10²².