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

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three persons apply for the same house is

In a single throw of two dice,what is the probability of obtaining an odd number as the sum of the numbers on the two dice?

An integer $x$ is chosen at random from $1$ to $50$. The probability that $x + \frac{336}{x} \leq 50$ is

If the events $A$ and $B$ are independent,and $P(A^{\prime}) = \frac{2}{3}$ and $P(B^{\prime}) = \frac{2}{7}$,then $P(A \cap B)$ is equal to:

The probability that a person $A$ completes a work in a given time is $\frac{2}{3}$ and the probability that another person $B$ completes the same work in the same time is $\frac{3}{4}$. If both $A$ and $B$ start doing this work at the same time,then the probability that the work is completed in the given time is