# Elementary Event and Compound Event

**Elementary Event :-**

An outcome of a random experiment is called an Elementary Event. Consider the random experiment of tossing of a coin. The possible outcomes of this experiment are head (H) or tail (T).Â Thus, if we defineÂ

E_{1} = Getting head (H) on the upper face of the coin,Â

and,Â

E_{2} = Getting tail (T) on the upper face of the coin.Â

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Then, E_{1} and E_{2} are elementary events associated with the experiments of tossing of a coin.

Let us consider the random experiment of tossing two coins simultaneously. The possible outcomes of this experiment are as under:

If we define,

HH = Getting head on both the coins

HT = Getting head on first and tail on secondÂ

TH = Getting tail on first and head on second

and, TT = Getting tail on both coins.Â

Then, HH, HT, TH and TT are elementary events associated with the random experiment of tossing of two coins.Â

Similarly, if three coins are tossed simultaneously, then the elementary events associated with this experiment are HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.Â

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Consider a cubical die marked with numbers, 1, 2, 3, 4, 5 and 6 on its six faces. Consider now the random experiment of throwing a cubical die. If the die is rolled, then any one of the six faces may come upward. So, there are six possible outcomes of this experiment, namely, 1, 2, 3, 4, 5, 6. Thus, if we define

E_{i} = Getting a face marked with number i, where i = 1, 2, â€¦ 6.Â

Then, E_{1}, E_{2}â€¦E_{6} are six elementary events associated to this experiment.Â

In this experiment, elementary event E_{i} is generally denoted by i, where i = 1, 2, 3 â€¦6.Â

Consider the random experiment in which two six faced dice are rolled together or a dice is rolled twice.

If (i, j) denotes the outcome of getting number i on first dice and number j on second dice, the possible outcomes of this experiment are:

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(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)

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Clearly, these outcomes are elementary events associated with the random experiment of throwing two six faced dice together. The total number of these elementary events is 36.

If a card is drawn from a well-shuffled pack of 52 cards, any one of the 52 cards can be the outcome. So there are 52 elementary events associated to the random experiment of drawing a card from a pack of 52 playing cards.

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**Compound Event :-**

An event associated to a random experiment is a compound event if it is obtained by combining two or more elementary events associated to the random experiment.

In a single throw of a dice, the event "getting an even number" is a compound event as it is obtained by combining three elementary events, viz., 2, 4, 6. Similarly, "getting an odd number" is a compound event in a single throw of a die.

Consider the random experiment of tossing two coins simultaneously. If we define the event "getting exactly one head", then HT and TH are two elementary events associated to it. So, it is a compound event.

Sample space: The set of all possible outcomes of an experiment is known as sample space.