CBSE Class 12 Maths

Probability

Each concept is a short lesson, then questions until you get three right.

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4 concepts, a short lesson each

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Conditional probability

$P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ : $B$ has happened, so $B$ is the new sample space

Conditional probability $P(A \mid B) = \frac{P(A \cap B)}{P(B)}$ : $B$ has happened, so $B$ is the new sample spaceStart
The multiplication theorem $P(A \cap B) = P(A)\,P(B \mid A)$ : draws without replacement change the second probabilityStart
Independent events $P(A \cap B) = P(A)\,P(B)$ ; "at least one" $= 1 - P(\text{none})$ Start
Total probability and Bayes' theorem $P(E_i \mid A) = \frac{P(E_i)P(A \mid E_i)}{\sum_j P(E_j)P(A \mid E_j)}$ : work backwards from the resultStart

Practise Probability

Once the concepts click, try the questions your exam asks.

Textbook exercisesEvery exercise, with model answers Past board questionsAsked from this chapter, with solutions