**Probability Class 9** notes are provided here to help students understand the concept of this topic more effectively. We can define probability as the measure of the likelihood that an event will occur. Or the number of favourable outcomes upon the total number of outcomes is defined as the probability of happening of any event. We can calculate the probability of a single event occurring, by dividing the number of events by the number of possible outcomes. In Class 9, you will come across the basic approach of **experimental probability** such as its definition, formula, examples, etc. Also, we have provided here with some important questions to practice for the exam.

## Probability Definition

Probability is basically the chances of an event to occur.Â The probability P(E) of an event E is determined by:

P(E) = Number of trials in which Event has happened/Total number of trials |

The Probability of any event always lies between 1 and 0.

### Experimental Probability

Empirical probability or experimental probability is based on genuine experiments and satisfactory recordings of the occurrence of events. To determine the happening of any event, a series of real experiments are conducted. Experiments which do not have a fixed result are called random experiments. The result of such events is uncertain. Random experiments are repeated multiple times to determine their probability. An experiment is repeated a fixed number of times and each repetition is known as a trial.

**Experimental Probability = Number of times an event occurs / Total number of trials**

### Events in Probability

There are basically three types of events occurring in probability.

- Complimentary Event
- Events associated with ‘OR’
- Events associated with ‘AND’

### Example of Probability

**A coin is tossed 100 times resulting in the following frequencies: Heads 45 times and Tail 55 times. For calculating the probability of all possible events let us assume â€˜Hâ€™ as an event of getting a head and â€˜Tâ€™ as an event of getting a tail. Then, the probability of getting heads:**

P (H) =Number of Heads/Total Number of Trials = 45/100 = 0.45

Similarly, the probability of getting a tail:

P (T) = Number ofÂ Tails/Total Number of Trials = 55/100 = 0.55

In the above example, the probability of getting tail P(T) + probability of getting heads P(H) = 0.45 + 0.55 = 1. Also, there are only 2 possible outcomes in each trial i.e. either heads or tails.

### Extra Questions for Practice

Q.1) A coin is tossed 1000 times with the following frequencies:

Tail: 545, and Head: 455. Calculate the probability for each event.

Q.2) A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3,

4, 5 and 6 as given in the table below:

Outcome | 1 | 2 | 3 | 4 | 5 | 6 |

Frequency | 179 | 150 | 157 | 149 | 175 | 190 |

Find the probability of getting each outcome.

Q.3) The percentage of marks obtained by a student in the monthly unit tests

are mentioned in the table below:

Test | 1 | 2 | 3 | 4 | 5 |

Marks | 78 | 76 | 89 | 90 | 81 |

Find the probability that the student gets more than 80% marks in a unit test based on the given data.

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