Maths

Class 12

Maths · Class 12 · Chapter 13

Probability

10 lessons 84 min 2 simulations

Class XI probability treated each event on its own. This chapter asks what happens to the probability of an event once some other event is known to have occurred. That is conditional probability, P(E|F) = P(E ∩ F)/P(F), and everything else grows out of it. Turning the definition around gives the multiplication theorem for P(E ∩ F). Events whose probabilities do not react to each other are called independent, and for them P(E ∩ F) = P(E) P(F). When the sample space is cut into non-overlapping cases (a partition), the theorem of total probability adds up an event's probability case by case, and Bayes' theorem runs the condition backwards: from the chance of the evidence under each case to the chance of each case given the evidence. The chapter closes with a remark on random variables, which JEE carries a step further.

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What the exam asks

Probability is not part of NEET. For JEE Main it is a regular source of questions, and almost all of them use this chapter: conditional probability read from a reduced sample space, the multiplication theorem for draws without replacement, independence (and the difference between independent and mutually exclusive), total probability with a tree, and Bayes' theorem for bag, machine and test problems. Marks are lost by confusing P(A|B) with P(B|A), by multiplying P(A) and P(B) for events that are not independent, by forgetting that the second draw depends on the first, and by leaving a case out of the denominator in Bayes' theorem. Board papers ask for the same problems with the events named and every step written.

Lessons

10 lessons · 84 min