Tag: events and its algebra

The set of all the possible outcomes is called the sample space of the experiment and is usually denoted by S. Any subset E of the sample space S is called an event. Here are some examples. Example 1 Tossing a coin

Choosing $4$ face cards in spades as well as rolling a die for $7$ are both impossible events.
The number of face cards in spades $= 3$ (king, queen, jack)

Choosing a queen from a deck of cards is an example of compound event.
Because the total number of card $= 52$
Choosing a queen card $= 4$ (spade, diamond, heart, club)
So, more than one element of the sample space in the set representing an event, then this event is called a compound event.

The probability of an event which is sure to occur at every performance of an experiment is called a certain event.
Example: Head or Tail is a certain event connected with tossing a coin.

The probability of an event is greater than or equal to $0$ and less than or equal to $1$.

The outcomes of a random experiment are called events connected with the experiment.
Example: $1, 2, 3, 4, 5, 6$ are the outcomes of the random experiment of rolling a dice and hence are events connected with it.

When the dice are thrown, the event $E = {4}$ then this event is called simple event.
If there be only one element of the sample space in the set representing an event, then this event is called a simple or elementary event.

The sample space in the set representing an event more than one element is called compound event.
Example: if we throw a dice, having $S = {1, 2, 3, 4, 5, 6}$, the event of a even number being shown is given by $E = {2, 4, 6}$.

Event is called one or more outcomes of an experiment.
Example: rolling a dice, we get a possible outcomes as ${1, 2, 3, 4, 5, 6}$.

Sample space for a die $= {1, 2, 3, 4, 5, 6} = 6$
Odd numbers $= 1, 3, 5 = 3$
So, $P$ (Odd number) $=$ $\dfrac{3}{6}= \dfrac{1}{2}$