Probability is a topic of great importance for the JEE Main exam. Students can expect 2-3 questions from probability for board exams and other competitive exams. So they are advised to learn the concept of probability so that they can easily crack the questions from this topic. Previous years’ questions and solutions on probability and important formulas of probability are available online in pdf format for free. Students are recommended to download and make use of these resources.
When we are not sure about an event, we talk about probability. Probability refers to the chance of occurrence of an event. The value of probability lies between 0 and 1. In this article, we will discuss how to find probability of an event. Following are some real-life examples of probability:
- Weather forecasting
- Flipping a coin
- Insurance
- Playing cards
Formula
The probability of an event is given by the ratio of the number of favourable outcomes to the total number of outcomes.
Probability = Number of favourable outcomes / Total number of outcomes.
While learning probability, we come across different types of events like dependent events, independent events, mutually exclusive events, etc. Students often get confused on how to find probability of an event, when events are dependent, independent etc. So they are advised to learn the concepts thoroughly.
Dependent and Independent Events
We can say that two events P and Q are independent if the probability of occurrence of P does not depend on the probability of occurrence of Q. If the outcome of P depends on the outcome of Q, then they are dependent events. Events that cannot occur at the same time are termed as mutually exclusive events.
Simple and Compound Events
An event is called a simple event if the sample space consists of a single point. Compound events are events having more than one point of the sample space. For example, if the sample is given by {10, 20, 25, 30}, then E = {25} is a simple event, E1 = {10, 20} is a compound event.
How to Find the Roots of a Quadratic Equation
We know that a quadratic equation is of the form ax2 + bx + c = 0, where a ≠ 0 and a, b, c∈R. There are different methods of solving quadratic equations. We will discuss how to find the roots of a quadratic equation along with the nature of roots. An easy method of solving a quadratic equation is by using the quadratic formula. It is given by x = [-b±√(b2-4ac)]/2a. Here, D = b2-4ac, called the discriminant. The value of D determines the nature of roots. If D is positive, then the roots are real and distinct. The roots are imaginary if D is negative. The roots are equal and real if D equal to zero.
Students are recommended to revise and practise previous years’ questions so that they can be familiar with the type of questions asked from quadratic equation and probability. Visit BYJU’S for important formulas pdf on quadratic equation and previous years’ JEE solved question papers.