It is known that 3% of plastic bags manufactured in a factory are defective. Using the Poisson distribution on a sample of 100 bags, the probability of at most one defective bag is:

Two cards are drawn simultaneously from a well shuffled pack of 52 cards. Then variance of the number of kings is

A die is thrown once then,

Match List-I with List-II

Choose the correct answer from the options given below:

Let E and F are events associated with an experiment. If $P(E) = 0.4$, $P(F) = 0.8$ and $P(F|E) = 0.6$, then $P(E|F)$ 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.

Suppose that A and B are independent events with $P(A)=\dfrac{1}{7}$ and $P(B)=\dfrac{3}{7}$, then $P(A\cap B)$ is

Probability that a man speaks truth is $\frac{3}{4}$. He throws a die and reports that it is a six. The probability that it is actually a six is