If $A$ and $B$ are two independent events such that $\mathrm{P}\left(\mathrm{A}^{\prime}\right)=0.75, \mathrm{P}(\mathrm{A} \cup \mathrm{B})=0.65$ and $\mathrm{P}(\mathrm{B})=\mathrm{p}$, then value of $p$ is

The probability that a person who undergoes a bypass surgery will recover is 0.6 . the probability that of the six patients who undergo similar operations, half of them will recover is __________.

$A$ and $B$ are independent events with $P(A)=\frac{3}{10}$, $\mathrm{P}(\mathrm{B})=\frac{2}{5}$, then $\mathrm{P}\left(\mathrm{A}^{\prime} \cup \mathrm{B}\right)$ has the value

Minimum number of times a fair coin must be tossed, so that the probability of getting at least one head, is more than $99 \%$ is