Class 12 Mathematics — Chapter 7: PROBABILITY

What you'll learn

• ▸Concept of Conditional Probability
• ▸Formula for Conditional Probability
• ▸Properties of Conditional Probability
• ▸Applications in 'Equally Likely' Scenarios
• ▸Problem Solving with Population Data
• ▸Conditional Probability in Multi-Stage Experiments

Chapter Summary

--- PAGE 1 --- 12080CH13 Chapter 13 PROBABILITY ❖ The theory of probabilities is simply the Science of logic quantitatively treated. – C.S. PEIRCE ❖ 13.1 Introduction In earlier Classes, we have studied the probability as a measure of uncertainty of events in a random experiment. We discussed the axiomatic approach formulated by Russian Mathematician, A.N. Kolmogorov (1903-1987) and treated probability as a function of outcomes of the experiment. We have also established equivalence between the axiomatic theory and the classical theory of probability in case of equally likely outcomes. On the basis of this relationship, we obtained probabilities of events associated with discrete sample spaces. We have also studied the addition rule of probability. In this chapter, we shall discuss the important concept of conditional probability of an event given that another event has occurred, which will be helpful in understanding the Bayes' theorem, multiplication rule of probability and indepen…

Practice Questions from this Chapter

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1. Explain conditional probability simply. Get Solution →
2. Give real-world probability examples. Get Solution →
3. Calculate my chances of winning a coin flip game. Get Solution →
4. Who is credited in the text with formulating the axiomatic approach to probability? Get Solution →
5. What is the correct formula for the conditional probability of an event E given that event F has occurred? Get Solution →
6. For any event F from a sample space S, what is the value of P(S|F)? Get Solution →
7. What is the value of P(F|F) for any event F with P(F) > 0? Get Solution →
8. According to Property 3, what is the formula for P(E'|F), where E' is the complement of event E? Get Solution →

Did you know?

• 💡 The chance of two people sharing a birthday in a room of 23 is surprisingly over 50%.
• 💡 There are more ways to shuffle a deck of cards than atoms in the Milky Way galaxy.
• 💡 A computer-generated "random" number is never truly random, it uses a formula.
• 💡 The study of probability started with analyzing gambling games in the 17th century.
• 💡 The odds of getting struck by lightning in your lifetime are about 1 in 15,300.

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