The variance of number of heads in three tosses of a coin is :

A fair coin is tossed until a head or five tails occur. The probability distribution of the number of tosses 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 $A_1$ given that seed doesn't germinate.

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

A random variable X has the following probability distribution:

The value of $P(X\ge 3)$ is

A coin is tossed thrice, and events E and F are defined as:

E : "The first throw results in a head"

F : "The last throw results in tail"

Then, which of the following statements is true for events E and F?

If A and B are event such that $P(A)=\dfrac{1}{2}$, $P(B)=p$ and $P(A \cup B)=\dfrac{3}{5}$ then which of following statements is/are TRUE?

(A) Events A and B are independent if $p=\dfrac{1}{5}$

(B) Events A and B are independent if $p \in (0,1) \sim \left\{\dfrac{1}{5}\right\}$

(C) Events A and B are independent then $P(A \cap B)=\dfrac{1}{10}$

(D) Event A and B are independent then $P(A \cap B)=\dfrac{9}{10}$

Choose the correct answer from the options given below: