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} $