If $P(A) = \frac{3}{10}$, $P(B) = \frac{2}{5}$ and $P(A \cup B) = \frac{3}{5}$ then the value of $P(B|A) + P(A|B)$ is:

A four digit number is formed by using the digits 1, 2, 4 and 5 with no repetition. The probability that the number is divisible by 5, is

For two events A and B, if $P(A) = 0.6$, $P(B) = 0.5$ and $P(A\cup B) = 0.8$. Then which of the following statements are TRUE ?

A. $P(A\cap B) = 0.3$.

B. A and B are independent events.

C. $P(A'\cap B') = 0.2$.

D. A and B are mutually exclusive events.

Choose the correct answer from the options given below:

Four cards are drawn successively without replacement from a deck of 52 playing cards. The probability that all the four cards are king is:

A man is known to speak truth 3 out of 4 times. He throws a die and reports that it is four. The probability that it is actually four is

A fair coin is tossed 100 times. The probability of getting head an odd number of times is

Two percent of the bolts manufactured in a factory are found to be defective. Using the Poisson distribution, the probability that in a sample of 100 bolts chosen at random, exactly two will be defective, is: [Given $e^{-2}=0.135$]