Question
Define probability of an event.
✓
Answer
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 $\text{P(A)}=\frac{\text{m}}{\text{n}}$ To illustrate the definition, let us take examples:
- 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
$\text{P(A)}=\frac{\text{m}}{\text{n}}$
$=\frac{1}{4}$
$=0.25$
- 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
$\text{P(A)}=\frac{\text{m}}{\text{n}}$
$=\frac{3}{6}$
$=\frac{1}{2}$
$=0.5$
Note that H stands for getting a head and T stands for getting a tail in the experiment of tossing a coin.Need a full question paper?
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