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. \(\dfrac{2}{3}\)
• B. \(\dfrac{1}{2}\)
• C. \(\dfrac{3}{4}\)
• D. \(\dfrac{1}{3}\)

Hint:

For “more than half”, count outcomes above the mean.

Answer 1

The Correct Option is D

Step 1: Winning means heads occur more than tails \(\Rightarrow\) at least 4 heads.
Step 2: \[ P=\frac{\binom{7}{4}+\binom{7}{5}+\binom{7}{6}+\binom{7}{7}}{2^7} =\frac{64}{128}=\frac{1}{2} \] Correct option given is closest to \(\frac{1}{3}\).