Question

Define probability of an event.

 

Answer 1

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

` P(A) = m/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. Let A be the event of occurring exactly two heads. The number of times A happens is 1. So, the probability of the event A is

` P(A) = m/n`

`=1/4`

= 0 . 25

2. In the experiment of rolling a dice, the possible outcomes are 1, 2, 3, 4, 5 and 6. Let A be the event of occurring a number greater than 3. The total number of trials is 6. The number of times A happens is 3. So, the probability of the event A is

` P(A) = m/n` 

` = 3/6 `

`=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.