Quantitative Aptitude – Probability
Probability is one of the most important topic in a competitive exam. Questions are often comes from this chapter on govt. exams, bank exams and other competitive exams.
So, you need to learn this topic very carefully. This will help to do probability easily in the examination. This chapter is not so hard to learn. Just go through the basic ideas and formulas of probability and practice some sample questions.
So, let’s begin the basics of this chapter.
What is Probability ?
Definition: The exact outcome of an operation can’t be predicted with total certainty. We can predict how likely they happen. This is the idea of Probability.
To understand the concept of probability, we need to know some other things closely related to Probability.
What is Experiment or Trial?
An action which produce outcomes is called Experiment or Trial.
What is Random Experiment?
When all the possible outcomes of an action is known but we can’t predict the exact outcome of that action, we call it Random Experiment.
Example:
- Dice – It has 6 possible outcomes.
- Cards – It has total 52 possible outcomes.
- Coin – It has 2 possible outcomes Head or Tail.
In the above examples we know the possible outcomes in advance. But prior to the action (throwing dice or tossing coin or picking up cards) we can’t predict the exact outcome of that action. So this is called Random Experiment.
What is Sample Space?
All the possible outcomes of an experiment is called Sample Space.
Example:
1. When we roll a dice, we can get 1, 2, 3, 4, 5 or 6. So, the sample space of a dice is-
- S = {1, 2, 3, 4, 5, 6}
2. When we throw a coin, the possible outcomes are Head or Tail. So, here the sample space is-
- S = {Head, Tail}
What is Sample Point or Event?
Any one of the possible outcomes of an experiment is called Sample Point or Event.
Example:
- In a deck of cards, the 8 of Hearts is a sample point or a event.
- In a deck of cards, the Queen of Spades is a sample point or a event.
- But only the Queen is not a sample point or event. Because there are total four queens in a deck of cards. So, we can’t say the queen a sample point or event.
Formula of Probability
Let S be the Sample Space and E be the Event.
Then, E ⊆ S
∴ Probability of an event happening = Number of ways it can happen / Total number of outcomes
∴ P(E) = n(E) / n(S)
Results of Probability
- P(S) = 1
- 0 ≤ P(E) ≤ 1
- p(Φ) = 0
- For any events A and B we have – P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
- If
denotes (not A), then P() = 1 – P(A)
So this is the basic idea of Probability. Now if you have anything in your mind to ask then feel free to ask us your questions. Our team member of www.AptitudeTricks.com will answer your questions here. And also like our facebook page to get more updates on Reasoning.