The word probability or chance is extremely frequently utilized in day-to-day life. For example, we generally say, ‘He may come today or ‘probably it may rain tomorrow’ or ‘most probably he will get through the examination’. All these phrases involve an element of uncertainly and probability is a concept which measures the uncertainties. The probability when defined in the simplest way is the chance of occurring a certain event when expressed quantitatively, i.e., the probability is a quantitative measure of the certainty. Probability also means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from 0 to at least 1.
The probability has its origin within the problems handling games of chance like gambling, coin tossing, die throwing, and playing cards. In all these cases the outcome of a trial is uncertain. These days probability is widely used in business and economies in the field of predictions for the future.
For example, once we toss a coin, either we get Head or Tail, only two possible outcomes are possible (H, T). But if we toss two coins within the air, there might be three possibilities of events to occur, like both the coins show heads or both show tails or one shows heads and one tail, i.e.(H, H), (H, T),(T, T).
Formula for Probability
The probability formula is defined because the possibility of an occasion to happen is adequate to the ratio of the number of favorable outcomes and therefore the total number of outcomes.
Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes
Important terms and Concepts
- Random experiment or Trial: The performance of an experiment is called a trial. An experiment is characterized by the property that its observations under a given set of circumstances do not always lead to the same observed outcome but rather to the different outcomes. If in an experiment all the possible outcomes are known beforehand and none of the outcomes are often predicted with certainty, then such an experiment is named a random experiment.
- Equally Likely Events: Events are said to be equally likely if there is no reason to accept anyone in preference to others. Thus, equally likely events mean the outcome is as likely to occur as the other outcome.
- Simple and Compound Events: In the case of simple events we consider the probability of happening or non-happening of single events and in the case of compound events we consider the joint occurrence of two or more events.
- Exhaustive Events: It is the total number of all possible outcomes of any trial.
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Algebra of Events: If A and B are two events associated with sample space S, then
- A ∪ B is that the event that either A or B or both occur.
- A ∩ B is the event that A and B both occur simultaneously.
- Mutually Exclusive Events: In an experiment, if the occurrence of an occasion precludes or rules out the happening of all the opposite events in the same experiment.
- Probability of an Event: Assume an event E can occur in r ways out of a sum of n probable or possible equally likely ways. Then the probability of happening of the event or its success is expressed as;
P(E) = r/n
The probability that the event won’t occur or referred to as its failure is expressed as:
P(E’) = (n-r)/n = 1-(r/n)
E’ represents that the event won’t occur.
Therefore, now we can say;
P(E) + P(E’) = 1
This means that the entire of all the possibilities in any random test or experiment is adequate to 1.
How to find the mean of a set of numbers?
To find the first moment of a knowledge set, all you would like to try to do is add up all the numbers within the data set then divide the sum by the total number of values.
For example, you’re given the subsequent data set:
3, 4, 5, 1, 2, 6, 7, 3, 9, 8, 11, 15
To find the mean first of all we have to add all the numbers as shown below:
3+4+5+1+2+6+7+3+9+8+11+15 = 74.
Note: To find the mean we need not arrange the data set in ascending order.
Now the last step is to take the sum and divide it by the total number of values in the given data set and we get,
74/12 = 6.166
Therefore, the mean of the given data set is 6.166.
Sample Questions
Question 1. Find the mean of the following data set: 12, 23, 1, 2, 6, 7, 9, 5, 4.
Answer:
To find the first moment of a knowledge set, all you would like to try to do is add up all the numbers within the data set then divide the sum by the total number of values.
For example, you’re given the subsequent data set:
12, 23, 1, 2, 6, 7, 9, 5, 4
To find the mean first of all we have to add all the numbers as shown below:
12+23+1+2+6+7+9+5+4 = 69
Now the last step is to take the sum and divide it by the total number of values in the given data set and we get,
69/9 = 7.666
Therefore, the mean of the given data set is 7.666.
Question 2. Find the mean of the following data set: 5, 26, 9, 14, 49, 31, 201, 5.
Answer:
To find the first moment of a knowledge set, all you would like to try to do is add up all the numbers within the data set then divide the sum by the total number of values.
For example, you’re given the subsequent data set:
5, 26, 9, 14, 49, 31, 201, 5
To find the mean first of all we have to add all the numbers as shown below:
5+26+9+14+49+31+201+5 = 340
Now the last step is to take the sum and divide it by the total number of values in the given data set and we get,
340/8 = 42.5
Therefore, the mean of the given data set is 42.5.
Question 3. Find the mean of the following data set:15, 15, 21, 30, 35, 41.
Answer:
To find the first moment of a knowledge set, all you would like to try to do is add up all the numbers within the data set then divide the sum by the total number of values.
For example, you’re given the subsequent data set:
15, 15, 21, 30, 35, 41
To find the mean first of all we have to add all the numbers as shown below:
15+15+21+30+35+41 = 157
Now the last step is to take the sum and divide it by the total number of values in the given data set and we get,
157/6 = 26.166
Therefore, the mean of the given data set is 26.166.