Probability is the measurement of the possibility of any event. Its value always lies between 0 and 1. It is used to make predictions for likely random events to happen. If we say this in slightly different words, then probability is a method with the help of which we can know the number of chances of getting one or more outcomes for any event happening in the world. What is this probability? Let us understand this with an example. Suppose we buy a light bulb. What is the percentage chance that the light bulb will be defective? Now there is only one light bulb and the chances of it being defective or not are 50%. But if there are more light bulbs and there are some other conditions as well, such as if three light bulbs are purchased together, all three have different colors, and if any of them is defective, it must be a particular colored light bulb. Then, the prediction of possibility becomes a bit difficult. That is why probability methods are used to measure the possibilities of different events.
Various methods of probability are learned through simple and conditional events like tossing a coin or rolling a die.
The most basic formula of probability of an event is given by,
PROBABILITY = Number of favorable events / Total number of events
Let’s understand it with an example of rolling a dice. If 6 6-faced dice is rolled, then it may produce 6 different outputs from 1 to 6. If, in such a case, we need to find the chances of getting number 2 in output, then here, the total number of events will be 6, and the number of favorable events will be 1 because we need a particular number in the output.
We also need to know about the concept of conditional probability because it is associated with two events occurring together, and one event completely depends on another event. Let’s understand it with an example,
Suppose in a company 50 people work, among which 20 people work in the accounts department and 15 people work in the sales department and 10 people work in both the department. Now if a person is chosen at random from the accounts department, then what is the probability that the chosen person also works in the sales department?
In this example, we need to find the probability that the chosen person works in the sales department when it is given that he already works in the accounts department. It is a situation of two mixed events where one event is completely dependent on another event.
The conditional probability has a mathematical representation also. If there are two events A and B, then P(`\frac{A}{B}`) represents the conditional probability for event A, and it is given by,
P(`\frac{A}{B}`) = P(A⋂B)/P(B)
Here, P(A⋂B) represents the probability of common values between events A and B. It is a good formula, but the best way to find the conditional probability is to analyze events using basic counting methods.
A very important concept in the probability that everyone always needs to remember is that the sum of the probability of favorable events and the probability of non-favorable events is always 1. Let’s understand it with the above example of rolling a dice. If P is the probability of getting the number 2 in output and P̅ is the probability of not getting the number 2 in output, then
P + P̅ = 1
In the real world, we can make very accurate observations about any event with the help of probability. But it requires a lot of practice, and practice comes from continuously solving questions. That is why, on this website, you will find numerous practice questions with their detailed solutions related to probability and other topics of mathematics. These practice questions will be very useful for various competitive exams like IITJEE, GATE, CAT, GMAT, etc. So, find questions according to your topic and practice as much as you want.
.png)
0 Comments