Question

A coin is tossed $7$ times. Each time a man calls head. Find the probability that he wins the toss on more occasions.

• A. $\frac{2}{3}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{1}{3}$

Answer 1

Answer: (B)

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