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The probability of all possible outcomes of a random experiment is always equal to ______.

100

One

Zero

Infinity

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Correct option is B)

Probability shows the relationship between two variables in the form of ratio, percentage or proportion where there the chances of occurrence of one variable is expressed in terms of the given sample space that consist of the occurrence of all related variable.. Since the value variable belongs to all possible outcomes of a random experiment, the probability of such an event will be 1.

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The probability of all possible outcomes ofa a random experiment is always equal to

The probability of all possible outcomes ofa a random experiment is always equal to

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The probability of all possible outcomes ofa a random experiment is always equal to

Updated On: 27-06-2022

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Random Experiments

The outcome of a random experiment is uncertain. We describe the set of all possible outcomes with probability

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1.3.1 Random Experiments

Before rolling a die you do not know the result. This is an example of a random experiment. In particular, a random experiment is a process by which we observe something uncertain. After the experiment, the result of the random experiment is known. An outcome is a result of a random experiment. The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our . Here are some examples of random experiments and their sample spaces:

Random experiment: toss a coin; sample space:

S={heads,tails} S={heads,tails}

or as we usually write it,

{H,T} {H,T} .

Random experiment: roll a die; sample space:

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

Random experiment: observe the number of iPhones sold by an Apple store in Boston in

2015 2015 ; sample space: S={0,1,2,3,⋯} S={0,1,2,3,⋯} .

Random experiment: observe the number of goals in a soccer match; sample space:

S={0,1,2,3,⋯} S={0,1,2,3,⋯} .

When we repeat a random experiment several times, we call each one of them a trial. Thus, a trial is a particular performance of a random experiment. In the example of tossing a coin, each trial will result in either heads or tails. Note that the sample space is defined based on how you define your random experiment. For example,

Example

We toss a coin three times and observe the sequence of heads/tails. The sample space here may be defined as

S={(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H),(T,T,T)}.

S={(H,H,H),(H,H,T),(H,T,H),(T,H,H),(H,T,T),(T,H,T),(T,T,H),(T,T,T)}.

Our goal is to assign probability to certain events. For example, suppose that we would like to know the probability that the outcome of rolling a fair die is an even number. In this case, our event is the set

E={2,4,6} E={2,4,6}

. If the result of our random experiment belongs to the set

E E

, we say that the event

E E

has occurred. Thus an event is a collection of possible outcomes. In other words, an event is a subset of the sample space to which we assign a probability. Although we have not yet discussed how to find the probability of an event, you might be able to guess that the probability of

{2,4,6} {2,4,6} is 50 50

percent which is the same as

1 2 12

in the probability theory convention.

Outcome: A result of a random experiment.

Sample Space: The set of all possible outcomes.

Event: A subset of the sample space.

If A A and B B are events, then A∪B A∪B and A∩B A∩B

are also events. By remembering the definition of union and intersection, we observe that

A∪B A∪B occurs if A A or B B occur. Similarly, A∩B A∩B occurs if both A A and B B

occur. Similarly, if

A 1 , A 2 ,⋯, A n A1,A2,⋯,An

are events, then the event

A 1 ∪ A 2 ∪ A 3 ⋯∪ A n A1∪A2∪A3⋯∪An

occurs if at least one of

A 1 , A 2 ,⋯, A n A1,A2,⋯,An occurs. The event A 1 ∩ A 2 ∩ A 3 ⋯∩ A n A1∩A2∩A3⋯∩An occurs if all of A 1 , A 2 ,⋯, A n A1,A2,⋯,An

occur. It can be helpful to remember that the key words "or" and "at least" correspond to unions and the key words "and" and "all of" correspond to intersections.

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