A pair of fair dice is thrown 4 times. If getting the same number on both dice is considered as a success, then the probability of two successes are

A family has 3 children. The probability that all the three children are girls, given that at least one of them is a girl is

If a random variable X has the following probability distribution of X

$$ \begin{array}{|l|c|c|c|c|c|c|c|c|} \hline \mathrm{X}=x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \mathrm{P}(\mathrm{X}=x) & 0 & \mathrm{k} & 2 \mathrm{k} & 2 \mathrm{k} & 3 \mathrm{k} & \mathrm{k}^2 & 2 \mathrm{k}^2 & 7 \mathrm{k}^2+\mathrm{k} \\ \hline \end{array} $$

Then $P(x \geq 6)=$

If $X \sim B\left(6, \frac{1}{2}\right)$, then $P(|X-2| \leqslant 1)=$