Probability-6

Consider the probability of obtaining equal number of heads and tails . This amounts to ${ 6 \choose 3} (\frac{1}{2})^6$ ( Call this $Y$ )

Now , it is equally likely that number of tails is greater than heads / lesser than number of heads

Hence probability that number of tails is more than number of heads is

$\displaystyle \large \frac{1 - Y } {2} = \frac{22}{64}$