## What is Probability?

We can define probability as the measure of the likelihood that an event will occur. We can calculate the probability of a single event occurring by dividing the number of events by the number of possible outcomes. Probability Class 9 notes are provided here to help students understand the concept of this topic more effectively.

The probability P(E) of an event E is determined by:

P(E) = \(\frac{Number \;of\; trials\; in\; which \;E\; has\; happened }{Total\; number\; of \;trials}\)

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

### 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 ‘H’ as an event of getting a head and ‘T’ as an event of getting a tail. Then, the probability of getting heads:

P (H) = \(\frac{Number \;of\; Heads }{Total\; number\; of \;trials}\;=\;\frac{45}{100}\;=\;0.45\)

Similarly, the probability getting a tail:

P (T) = \(\frac{Number \;of\; Tail }{Total\; number\; of \;trials}\;=\;\frac{55}{100}\;=\;0.55\)

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.

### Important Questions

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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