Bernoulli Trials and Binomial Distribution

How many times a fair coin must be tossed so that the probability of having at least one head is more than $90\%$ ?

If a fair coin is tossed $10$ times, find the probability of exactly five heads.

$A$ and $B$ throw a die alternatively till one of them gets a $6$ to win the game. Find their respective probability of winning if $A$starts first.