Sample Space and Event in Probability

Sample Space and Event in Probability:

Sample Space- The set of all possibilities of a random experiment is called its sample space. A sample space is denoted by ‘S’.

Example- (i) When a coin is tossed-

S = { H, T }

(ii) When a coin is tossed two times or two coins tossed simultaneously-

S = { HH, HT, TH, TT }

(iii) When a coin is tossed three times or three coins are tossed simultaneously-


(iv) When a coin is tossed ‘n’ times, then n(S) = 2n.

(v) When a die is rolled-

S = { 1, 2, 3, 4, 5, 6 }

(vi) When two die are rolled-

sample space probability

(vii) When a die is rolled n times then (S) = 6n.

(viii) A die is rolled. When it shows an even number, a coin is tossed. Construct the sample space.

S = { 1, (2, H) (2, T), 3, (4, H) (4, T), 5, (6, H) (6, T) }

Event- Any subset of the sample space is called an event. An event is denoted by A, B, C, ……..

Types of Events:

(i) Simple Event- A single possible outcome of an experiment is called a simple event. If three die are thrown together then the events { 6, 6, 6, }, { 1, 2, 3 } etc., are simple events. Simple events are sometimes referred to as indecomposable event or elementary event.

(ii) Compound Event- The joint occurrence of two or more simple events is called a compound event. Thus, in the case of three tosses of a coin, the event corresponding to the statement “getting at least two tails” is given by { TTH, THT, HTT, TTT } and is a compound event which is also a decomposable event.

(iii) Sure Event- An event that is bound to happen is called a sure event. If the event is equal to its sample space then the event is called a sure event. In the case of a throw of a die, the event S = { 1, 2, 3, 4, 5, 6 } is a sure event because one of the outcomes from S must occur.

(iv) Impossible Event- An event corresponding to the empty set is called an impossible event. In the case of a throw of die “getting a number more than 6”, “getting a number less than 1” or in the case of a throw of two die together, “getting a sum more than 12” etc. are examples of impossible events.

(v) Exhaustive Events- If the events E1, E2, ……, En of a trial be such that E1 ∪ E2 ∪ …… ∪ En = S (sample space), then the events E1, E2, ……, En are called exhaustive events. In the case of a toss of a coin, if E1 = { H }, E2 = { T }, then E1 ∪ E2 = { H, T } = S. So, E1 and E2 are totally exhaustive events.

(vi) Mutually Exclusive Events- If A and B be two events such that the occurrence of A does not affect the occurrence of B then A and B are mutually exclusive events i.e. A and B are mutually exclusive if A ∩ B = Φ.

(vii) Complementary Event- The complement of an event A, denoted by Ā or A’ or Ac, is the set of all sample points of the space other than the space denoting event A. Thus, Ac = S – A.

(viii) Independent Events- When the outcome of the first event does not influence the outcome of the second event, those events are known as independent events. Example- The event of getting a tail after tossing a coin and the event of getting a head when tossing another coin.

Tangent Galvanometer
Moving Coil Galvanometer
Faraday’s Laws of Electromagnetic Induction
AC Generator or Dynamo
DC Generator or DC Dynamo
Young’s Double Slit Experiment
Wheat Stone Bridge Principle
Potentiometer and its Application
Zeroth Law of Thermodynamics
Variation of Resistance with Temperature
Nomenclature and General Principles– NIOS

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