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Question
Define probability of an event.
Solution
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.
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