Question
Define probability of an event.
✓
Answer
The probability of an event denotes the relative frequency of occurrence of an experiment’s outcome, when repeating the experiment.
Definition:
The empirical or experimental definition of probability is that if $n$ be the total number of trials of an experiment and $A$ is an event associated to it such that $A$ happens in $m-$trials, then the probability of happening of event $A$ is denoted by $P(A)$ and is given by $\text{P(A)}=\frac{\text{m}}{\text{n}}$ To illustrate the definition, let us take examples:
$1.$ When two coins are tossed simultaneously, the possible outcomes are $HH, HT, TH$ and $TT.$
The total number of trials is $4.$
$2.$ Let $A$ be the event of occurring exactly two heads.
$3.$ The number of times $A$ happens is $1.$
$4.$ So, the probability of the event $A$ is
$\text{P(A)}=\frac{\text{m}}{\text{n}}$
$=\frac{1}{4}$
$=0.25$
$1.$ In the experiment of rolling a dice, the possible outcomes are $1, 2, 3, 4, 5$ and $6.$
$2.$ Let $A$ be the event of occurring a number greater than $3.$
$3.$ The total number of trials is $6.$ The number of times $A$ happens is $3.$
$4.$ So, the probability of the event $A$ is
$\text{P(A)}=\frac{\text{m}}{\text{n}}$
$=\frac{3}{6}$
$=\frac{1}{2}$
$=0.5$
Note that $H$ stands for getting a head and $T$ stands for getting a tail in the experiment of tossing a coin.
Definition:
The empirical or experimental definition of probability is that if $n$ be the total number of trials of an experiment and $A$ is an event associated to it such that $A$ happens in $m-$trials, then the probability of happening of event $A$ is denoted by $P(A)$ and is given by $\text{P(A)}=\frac{\text{m}}{\text{n}}$ To illustrate the definition, let us take examples:
$1.$ When two coins are tossed simultaneously, the possible outcomes are $HH, HT, TH$ and $TT.$
The total number of trials is $4.$
$2.$ Let $A$ be the event of occurring exactly two heads.
$3.$ The number of times $A$ happens is $1.$
$4.$ So, the probability of the event $A$ is
$\text{P(A)}=\frac{\text{m}}{\text{n}}$
$=\frac{1}{4}$
$=0.25$
$1.$ In the experiment of rolling a dice, the possible outcomes are $1, 2, 3, 4, 5$ and $6.$
$2.$ Let $A$ be the event of occurring a number greater than $3.$
$3.$ The total number of trials is $6.$ The number of times $A$ happens is $3.$
$4.$ So, the probability of the event $A$ is
$\text{P(A)}=\frac{\text{m}}{\text{n}}$
$=\frac{3}{6}$
$=\frac{1}{2}$
$=0.5$
Note that $H$ stands for getting a head and $T$ stands for getting a tail in the experiment of tossing a coin.
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