Empirical probability is one of the objective probabilities. It is the relative frequency of the occurrence of an event and is determined by actual observation of an experiment. Consider an experiment, event A occurs "f" number of times if we repeat experiment n times.

Then $\frac{f}{n}$ is known as frequency ratio. The particular limiting value from the frequency ratio as the number of repetitions becomes infinitely large is known as probability of the given event.

Probability is divided into two parts: theoretical probability and empirical probability. Sometimes empirical probability named as experimental probability. The probability of an event will always be a number between zero and one. An empirical probability of zero (0) means that the event never occurred and one (1) means that the event always occurred. In this section will study about empirical probability formula in detail.

Then $\frac{f}{n}$ is known as frequency ratio. The particular limiting value from the frequency ratio as the number of repetitions becomes infinitely large is known as probability of the given event.

Probability is divided into two parts: theoretical probability and empirical probability. Sometimes empirical probability named as experimental probability. The probability of an event will always be a number between zero and one. An empirical probability of zero (0) means that the event never occurred and one (1) means that the event always occurred. In this section will study about empirical probability formula in detail.

Empirical probability formula = Probability of an event happening is the ratio of the time similar events happened in the past.

or Empirical probability = $\frac{Number\ of\ times\ event\ occurs}{Total\ number\ of\ times\ experiment\ performed}$

X |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |

F |
2 | 15 | 29 | 57 | 70 | 59 | 20 | 10 | 8 |

Calculate the probability of occurred tails:

Total number of heads occurred in an experiment = 2 + 15 + 29 + 57 + 70 + 59 + 20 + 10 + 8 = 270

From given table, number of required cases = 59

Therefore P( tails equal to 5) = $\frac{59}{270}$ =

From given table, number of favorable cases = 2 + 15 + 29 + 57 = 103

Therefore P(tails less than 4) = $\frac{103}{270}$ =

Total number of cases = 10 + 8 = 18

So P(tails more than 6) = $\frac{18}{270}$ =

Marks |
100-120 |
120-140 |
140-160 |
160-180 |
180-200 |

No. of Students |
63 | 142 | 500 | 320 | 175 |

Find the probability that a student selected has marks :

Total marks obtained by students = 63 + 142 + 500 + 320 + 175 = 1200

There are 63 + 142 = 205 students.

$\therefore$ P(student scored marks under 140)= $\frac{205}{1200}$ =

There are 175 students.

$\therefore$ P(student scored marks above 180) = $\frac{175}{1200}$ =

There are 500 + 320 + 175 = 995 students.

$\therefore$ P(student scored marks between 140 and 200) = $\frac{995}{1200}$ =

The coin is thrown 100 times. So total number of trails =100

Given head occurs 12 times. So the number of times the required event occurs = 12

Therefore probability of getting the event of head = $\frac{12}{100}$ = 0.12 (Using experimental probability formula)