The mean of the number of heads in the two tosses of a coin is

The random variable X can take values 0, 1, 2. If $P(X=0)=P(X=1)=\alpha$, and $E(X^2)=E(X)$, then which of the following are correct?

(A) $E(X) = 2-3\alpha$

(B) $E(X^2) = 4+7\alpha$

(C) $\alpha = \frac{1}{2}$

(D) $\alpha = \frac{1}{5}$

Choose the correct answer from the options given below:

The value of $k$ is

The probability that the study time of students is at least 1 hour

If A and B are two independent events such that $P(A) = \frac{4}{7}$ and $P(B) = \frac{2}{7}$ then $P(\overline{A} \cap \overline{B})$ equals

The probability distribution of a discrete random variable X is given as :

The value of K is:

A shopkeeper sells three types of flower seeds $A_1, A_2, A_3$. They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.

The probability that seed is of type $A_2$ given that seed germinate.