Mathematics - Probability Question with Solution | TestHub

The man has to win at least 4 times. $$\begin{array}{r}\therefore \text{ Reqd. probability }=\\ \begin{array}{r}7{\mathrm{C}}_4{\left(\frac{1}{2}\right)}^4\cdot {\left(\frac{1}{2}\right)}^3+{}^7{\mathrm{C}}_5{\left(\frac{1}{2}\right)}^5\cdot {\left(\frac{1}{2}\right)}^2\\ +{}^7{\mathrm{C}}_6{\left(\frac{1}{2}\right)}^6\cdot \frac{1}{2}+{}^7{\mathrm{C}}_7{\left(\frac{1}{2}\right)}^7\\ =\left({}^7{\mathrm{C}}_4+{}^7{\mathrm{C}}_5+{}^7{\mathrm{C}}_6+{}^7{\mathrm{C}}_7\right)\cdot \frac{1}{2^7}=\frac{64}{2^7}=\frac{1}{2}\end{array}\end{array}$$