Class 11 Mathematics — Chapter 14: PROBABILITY
Chapter 14: PROBABILITY is a chapter in Class 11 Mathematics (NCERT), part of the CBSE NCERT curriculum followed by over 25 million students across India. This chapter covers 5 topics including Events and Sample Space, Types of Events: Simple, Compound, Impossible, and Sure, Algebra of Events. BrainWeave provides free AI-powered explanations — by voice or text, in Hindi or English — with no signup required.
What you'll learn
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▸Events and Sample SpaceCore conceptsample spaceeventsubsetoutcomerandom experiment
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▸Types of Events: Simple, Compound, Impossible, and SureCore conceptsimple eventcompound eventimpossible eventsure eventelementary event
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▸Algebra of EventsCore conceptunionintersectioncomplementA or BA and B
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▸Mutually Exclusive EventsCore conceptmutually exclusivedisjoint setssimultaneouslyintersectionno common outcomes
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▸Exhaustive EventsCore conceptexhaustive eventsunionsample spaceat least onemutually exclusive and exhaustive
Chapter Summary
Understand that in a random experiment, the set of all possible outcomes is the sample space (S), and an event (E) is any subset of this sample space. Students must be able to list the sample space for a given experiment and represent a described event as a specific subset.
Differentiate between various fundamental types of events. A simple (or elementary) event contains a single outcome, a compound event contains multiple outcomes, an impossible event corresponds to the empty set (φ), and a sure event corresponds to the entire sample space (S).
Apply set theory operations to describe relationships between events. This includes the 'A or B' event (Union: A ∪ B), the 'A and B' event (Intersection: A ∩ B), the 'not A' event (Complement: A'), and the 'A but not B' event (Difference: A - B).
Define and identify mutually exclusive events, which are events that cannot occur at the same time. This is mathematically represented by their intersection being the empty set (A ∩ B = φ), meaning they are disjoint sets.
Define and identify a set of exhaustive events, which are events whose union covers the entire sample space (E₁ ∪ E₂ ∪ ... ∪ Eₙ = S). Students should also be able to determine if a set of events is both mutually exclusive and exhaustive.
Practice Questions from this Chapter
Tap "Get Solution" on any question to ask our AI tutor.
- Calculate my chances of winning. Get Solution →
- Explain 'sure event' simply. Get Solution →
- Compare mutually exclusive events. Get Solution →
- According to the text, any subset of a sample space S is called what? Get Solution →
- Which term describes an event that corresponds to the empty set φ? Get Solution →
- What type of event is represented by the entire sample space S? Get Solution →
- An event that has only one sample point from a sample space is called a... Get Solution →
- According to the text, what is the term for an event that has more than one sample point? Get Solution →
Did you know?
- 💡 Ancient civilizations used bone dice over 3000 years ago for games of chance.
- 💡 The 'Birthday Paradox' states two people in a group of 23 often share a birthday.
- 💡 A flipped coin slightly favors the side facing up before it is tossed.
- 💡 Weather forecasts use billions of probability calculations to predict future conditions.
- 💡 Your genetic traits follow specific probability patterns from your parents' DNA.
Frequently Asked Questions
How many topics are covered in this chapter?
This chapter covers 5 key topics: Events and Sample Space, Types of Events: Simple, Compound, Impossible, and Sure, Algebra of Events, Mutually Exclusive Events, Exhaustive Events. The BrainWeave AI tutor explains each one with examples.
Is Chapter 14: PROBABILITY important for board exams?
Class 11 is a foundation year. Mastering this chapter now will help you build strong fundamentals for the higher classes.
Can I get NCERT solutions for this chapter in Hindi?
Yes. BrainWeave's AI tutor supports Hindi, English, and Hinglish for both voice and text chat. Just ask your question in your preferred language.
Is BrainWeave free for Class 11 - Science?
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Can I use voice chat for this chapter?
Absolutely. Tap the mic, ask any question about Chapter 14: PROBABILITY, and the AI tutor will explain it back in voice and text.
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