A die is thrown, find the probability of following events: A number greater than or equal to $3$ will appear.
The sample space of the given experiment is given by
$S=\{1,2,3,4,5,6\}$
Let $B$ be the event of the occurrence of a number greater than or equal to $3$ . Accordingly,
$B =\{3,4,5,6\}$
$\therefore P(B)=\frac{\text { Number of outcomes favourable to } B }{\text { Total number of possible outcomes }}=\frac{n(B)}{n(S)}=\frac{4}{6}=\frac{2}{3}$
A coin is tossed $4$ times. The probability that at least one head turns up is
For three non impossible events $A$, $B$ and $C$ $P\left( {A \cap B \cap C} \right) = 0,P\left( {A \cup B \cup C} \right) = \frac{3}{4},$ $P\left( {A \cap B} \right) = \frac{1}{3}$ and $P\left( C \right) = \frac{1}{6}$.
The probability, exactly one of $A$ or $B$ occurs but $C$ doesn't occur is
A dice is thrown twice. The probability of getting $4, 5$ or $6$ in the first throw and $1, 2, 3$ or $4$ in the second throw is
From a pack of $52$ cards two cards are drawn in succession one by one without replacement. The probability that both are aces is
$2$ 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.