Applied Mathematics · Class 11 Commerce
Ch 9Probability — Class 11 Applied Mathematics, concept-first.
This concept map shows how the chapter fits together. Probability is the study of events — their types and the sample spaces they live in — and builds up to the theorem of total probability and Bayes' theorem for updating probabilities in the light of new evidence.
Key concepts
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Introduction
You've been solving problems your whole life. When you see a new type of question, you first figure out what it's asking, then decide which tools to use, then carry out the steps.
Most relevant Q&A
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Concept Map
This concept map shows how the chapter fits together. Probability is the study of events — their types and the sample spaces they live in — and builds up to the theorem of total probability and Bayes'…
Introduction
We encounter uncertainty every day — will it rain tomorrow, will a tossed coin land heads, will a new business succeed? Probability is the mathematical language we use to measure and reason about this…
Random Experiment and Sample Space
4 QA random experiment is any process whose outcome cannot be predicted with certainty in advance, even though the set of all possible outcomes is known.
+−Worked Examplesi2 questions
- Example 1In each of the following experiments specify appropriate sample space: (i) A girl has a one rupee coin, a two rupee coin and a five rupee co…Free
- Example 2A bag has 3 blue and 4 white balls in it. If a tossed coin shows head, we draw a ball from the bag. If it shows tail we throw a die to show…Preview
Event and Its Probability
An event is simply a subset of the sample space — a collection of outcomes we care about. For instance, in a single coin toss, getting a head is an event.
+−Exercise 9.2i5 questions
- Q1Give a real-life example of the following: Independent Events and Dependent Events.Free
- Q2Give a real-life example of the following: Impossible and Sure Events.Free
- Q3Give a real-life example of the following: Exhaustive Events.Preview
- Q4Give a real-life example of the following: Mutually Exclusive Events.Preview
- Q5Give a real-life example of the following: Mutually exclusive and exhaustive Events.Preview
Conditional Probability
3 QConditional probability answers a simple question: how does knowing one event has happened change the chance of another? For example, if you know it rained today, the probability that the ground is we…
+−Worked Examplesi1 question
+−Exercise 9.3i2 questions
Theorem of Total Probability
The Theorem of Total Probability is a powerful tool that lets you find the probability of an event by breaking it into cases — each case being a different "path" through a partition of the sample spac…
Bayes' Theorem
8 QBayes' Theorem is a powerful tool that flips conditional probability on its head — it lets you update your belief about a cause after you have seen its effect.
+−Exercise 9.5i6 questions
- Q1The number of loans sanctioned by a particular branch of a bank under different heads and the percentage of defaults in each category is giv…Free
- Q2A courier service company sends 30% of its orders by air, 50% by combination of bus and local transport and remaining 20% by train. Past rec…Free
- Q3A young entrepreneur imports high tech machines for a startup venture. The imported machines are to be set up by an expert who is sent by th…Preview
- Q4An insurance company insures scooter drivers, car drivers and bus drivers in the ratio 4:5:3. The probability of a scooter driver, car drive…Preview
- Q5Two cards from a pack of 52 cards are lost. From the remaining cards of the pack a card is drawn at random and is found to be spade. Find th…Preview
- Q6A laboratory blood test is 99% effective in detecting a certain disease when it is in fact, present. However, the test also yields a false p…Preview