The probability distribution of a random variable $X$ is given below

$$ \begin{array}{ccccccc} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline P\left(X=x_i\right) & \alpha & \alpha & \alpha & \beta & \beta & 0.3 \\ \hline \end{array} $$

If $\mu$ and $\sigma^2$ represent the mean and variance of $X$ and $\mu=4.2$, then $\sigma^2+\mu^2=$

The probability that a student gets distinction in a Mathematics test is $\frac{2}{3}$. If five such tests are conducted over a certain period of time, then the probability that he gets distinction in atleast 3 tests is

If $A$ and $B$ are events of a random experiment such that $P(A \cup B)=\frac{3}{4}, P(A \cap B)=\frac{1}{4}, P(\overline{\mathrm{~A}})=\frac{2}{3}$, then $P(\overline{\mathrm{~A}} \cap \mathrm{~B})=$

Two cards are drawn at random from a pack of 52 playing cards. If both the cards drawn are found to be black in colour, then the probability that atleast one of them is face card is