Introduction:
In online statistics free help , we say that there is a probability that something will happen when it is likely to happen. We often use phrases such as :
" There is a probability that it will rain today ", "There is a probability that he might be right" etc.
The statements :
"IT will rain today " , " He might be right " are the events (or situations) about which have an element of uncertainity in our mind, that the event may happen or may not happen.
The element of uncertainity about happening and non-happening of an event can be measured mathematically.
The branch of Mathematics, which deals with it, is called Theory of Probability.
Different Approaches :
There are following three approaches to theory of probability:
(i) Experimental approach or Empirical approach or Observed frequency approach.
(ii) Classical approach.
(iii) Axomatic approach.
Simple Definitions
Random Experiment :
Doing a trial is called Random experiment.
Example: (i) Toss a coin . (ii) Throw a die (iii) Pick a card from a pack of cards. etc.
Event :
Collection of some outcomes of the possible outcomes of a random experiment is called event.
Empirical Probability :
Let E be an event of happening. P(E) denotes the empirical probability for the happening of event E.
P(E) = $\frac{m}{n}$` where m = number of trial in which the event E happens and n = The total number of trials made.`
`Sure Event or Certainity :`
` When all the outcomes of a random experiment favour an event, the event is called a sure event and its empirical probability is ' 1 ' .`
`Impossible Event :`
` When no outcome of a random experiment favours an event, the event is called an impossible event and its empirical probability is ' 0`` ' .`
`Remarks :`
(i) P(E) + P( not-E) = 1
(ii) 0$\le$ P(E) $\le$ 1
(iii) Sum of the probabilities of all the outcomes of a random experiment is 1.
Simple Problems
The solved statistics problems gives more understanding on the concpet.
Q1 : There are 40 students in a class and their results is presented as below :
| Result (pass / Fail) | Pass | Fail |
| Number of Students | 30 | 10 |
If a student choosen at randoms out of the class, find the probability that the student has passed the examination.
Solution : Total number of chances = 40
Chances or trials which favour a student to pass = 30
The probability of the required event , i.e. the student has passed the examination = $\frac{30}{40}$ = 0.75
Q2 : In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that he did not hit a boundary .
Solution : Total number of balls he played = 30
Number of chances when the boundary is hit = 6
Number of chances when the boundary is not hit = 30 - 6 = 24.
The probability that he did not hit a boundary = $\frac{24}{30}$ = 0.8
Related Tags
Problems on Probability, What is Probability , Notes on Probability