A number is chosen at random from first ten natural numbers. The probability that number is odd and perfect square is
$\frac{2}{9}$
$\frac{2}{5}$
$\frac{3}{7}$
$\frac{1}{5}$
$2$ boys and $2$ girls are in Room $X$, and $1$ boy and $3$ girls in Room $Y$. Specify the sample space for the experiment in which a room is selected and then a person.
The probability of happening an event $A$ in one trial is $0.4$. The probability that the event $A$ happens at least once in three independent trials is
$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P ( A \cup B )$.
Three persons work independently on a problem. If the respective probabilities that they will solve it are $\frac{{1}}{{3}} , \frac{{1}}{{4}}$ and $\frac{{1}}{{5}}$, then the probability that none can solve it
A number is chosen at random from the set $\{1,2,3, \ldots, 2000\}$. Let $p$ be the probability that the chosen number is a multiple of $3$ or a multiple of $7$ . Then the value of $500\ p$ is. . . . . .