The mean of the number of heads in a simultaneous toss of three coins is

If A and B are two independent events, then which of the following is/are true?

(A) $P(A \cap B) = 0$

(B) $P(A \cup B) = 1 - P(A')P(B')$

(C) $P(A \cup B) = P(A)P(B)$

(D) $P(A \cap B) = P(A)P(B)$

Choose the correct answer from the options given below:

In the family mother, father and son stand up at random for a family picture. Define following two events :

$E$ = [Son stands at one of the two ends in the picture]

$F$ = [Father stands in the middle of the picture]

The value of $P(F/E)$ is :

If A and B are two events such that $A \neq \emptyset$, B $\neq \emptyset$, then which of following is/are TRUE:

A. $P(B/A)=P(A).P(B)$

B. $P(B/A)=\frac{P(A\cap B)}{P(A)}$

C. $P(A'/B')=\frac{1-P(A\cup B)}{1-P(B)}$

D. $P(B/A).P(A/B)=2$

Choose the correct answer from the options given below:

A problem in Mathematics is given to two students X and Y whose chances of solving it are $\frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that only X solves the problem, 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.

If A and B are independent events such that $P(A|B) = \frac{1}{3}$ and $P(B) = \frac{1}{2}$, then the value of $P(A \cap B)$ is equal to