{"id":7771,"date":"2022-04-20T09:37:57","date_gmt":"2022-04-20T04:07:57","guid":{"rendered":"https:\/\/www.goseeko.com\/blog\/?p=7771"},"modified":"2025-06-02T20:48:16","modified_gmt":"2025-06-02T15:18:16","slug":"what-is-the-sample-space-and-types-of-events%ef%bf%bc","status":"publish","type":"post","link":"https:\/\/www.goseeko.com\/blog\/what-is-the-sample-space-and-types-of-events%ef%bf%bc\/","title":{"rendered":"What is the sample space and types of events?\ufffc"},"content":{"rendered":"\n

Sample space<\/h2>\n\n\n\n

A sample space is the set of all possible outcomes of a random experiment. We denote it by S, and the total number of elements in the sample is the size of the sample space and we denote it by n(S).<\/p>\n\n\n\n

Discrete sample space- Sample space in which sample points are finite or countably infinite.<\/p>\n\n\n\n

For example-<\/p>\n\n\n\n

If we throw a dice, then the spl space is<\/p>\n\n\n\n

S = {1, 2, 3, 4, 5, 6} and n(S) = 6.<\/p>\n\n\n\n

If we toss a coin twice or simultaneously then-<\/p>\n\n\n\n

S = {HH, HT, TH, TT}<\/p>\n\n\n\n

If toss a coin 4 times or toss four coins simultaneously then-<\/p>\n\n\n\n

S = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTHT, HTTH, THHT,<\/p>\n\n\n\n

THTH, TTHH, HTTT, THTT, TTHT, TTTH, TTTT} and n(S) = 16.<\/p>\n\n\n\n

Note-If a random experiment with x possible outcomes is performed n times, then the total number of elements in the sample is x^n<\/p>\n\n\n\n

Events and their types <\/h2>\n\n\n\n

1. Exhaustive Events or Sample Space: The set of all possible outcomes of a single performance of an experiment is exhaustive events or sample space. Each outcome is a sample point.<\/p>\n\n\n\n

In case of tossing a coin once, S = (H, T) is the sample space. Two outcomes – Head and Tail<\/p>\n\n\n\n

– constitute an exhaustive event because no other outcome is possible.<\/p>\n\n\n\n

2. Trial and Event: Performing a random experiment is called a trial and outcome is termed an event. Tossing of a coin is a trial and the turning up of the head or tail is an event.<\/p>\n\n\n\n

3. Equally likely events: Two events are said to be \u2018equally likely\u2019, if one of them cannot be expected in preference to the other. For instance, if we draw a card from a well-shuffled pack, we may get any card. Then the 52 different cases are equally likely.<\/p>\n\n\n\n

4. Independent events: Two events may be independent, when the actual happening of one does not influence in any way the probability of the happening of the other.<\/p>\n\n\n\n

5. Mutually Exclusive events: Two events are known as mutually exclusive, when the occurrence of one of them excludes the occurrence of the other. For example, on tossing a coin, either we get head or tail, but not both.<\/p>\n\n\n\n

6. Compound Event: When two or more events occur in composition with each other, the simultaneous occurrence is called a compound event. When a die is thrown, getting a 5 or 6 is a compound event.<\/p>\n\n\n\n

7. Favorable Events: The events, which ensure the required happening, are said to be favorable events. For example, in throwing a die, to have the even numbers, 2, 4 and 6 are favorable cases.<\/p>\n\n\n\n

Odds in favor of an event and odds against an event-<\/p>\n\n\n\n

If the number of favorable cases are \u2018m\u2019 and the number or not favorable cases are \u2018n\u2019.<\/p>\n\n\n\n

Then-<\/p>\n\n\n\n

1. Odds in favor of the event = m\/n<\/p>\n\n\n\n

2. Odds against the event = n\/m<\/p>\n\n\n\n

Interested in learning about similar topics? Here are a few hand-picked blogs for you!<\/strong><\/p>\n\n\n\n