Suppose $A$ and $B$ are two events such that $P(A \cap B) = \frac{3}{25}$ and $P(B - A) = \frac{8}{25}$. Then, $P(B)$ is equal to

Suppose that a die (with faces marked $1$ to $6$) is loaded in such a manner that for $K = 1, 2, 3, 4, 5, 6$,the probability of the face marked $K$ turning up when the die is tossed is proportional to $K$. The probability of the event that the outcome of a toss of the die will be an even number is equal to

Let $A = \{1, 3, 5, 7, 9\}$ and $B = \{2, 4, 6, 8\}$. If an ordered pair $(a, b)$ is chosen at random from the Cartesian product $A \times B$,what is the probability that $a + b = 9$?

In each of the following experiments,specify the appropriate sample space: $A$ boy has a $1$ rupee coin,a $2$ rupee coin,and a $5$ rupee coin in his pocket. He takes out two coins out of his pocket,one after the other.

An experiment consists of rolling a die and then tossing a coin if the number on the die is even. If the number on the die is odd,the coin is tossed twice. Write the sample space for this experiment.

$A$ card is selected from a pack of $52$ cards. Calculate the probability that the card is a black card.