JEE Main 2026 — 2 April, Evening Shift — Question 30

$\mathrm{P}=(6$ tail $)+(4$ tail +1 head $)+(2$ tail +2 head $)+(3$ head $)$ $\mathrm{P}=\left(\frac{1}{2}\right)^{6}+\frac{5!}{1!4!}\left(\frac{1}{2}\right)^{5}+\frac{4!}{2!2!}\left(\frac{1}{2}\right)^{4}+\left(\frac{1}{2}\right)^{3}$ $\mathrm{P}=\frac{1}{64}+\frac{5}{32}+\frac{3}{8}+\frac{1}{8}$ $\mathrm{P}=\frac{1+10+24+8}{64}=\frac{43}{64}=\frac{\mathrm{m}}{\mathrm{n}}$ $\mathrm{m}+\mathrm{n}=107$