NCERT Mathematics, Class 12, textbook pages 406–438 (Part II)

How to help your child with Class 12 Maths Chapter 13, Probability, at home

Conditional probability, Bayes’ theorem and random variables, explained for parents: a 60-minute study session, a quick challenge, a 5-day plan and the mistakes to watch for.

0.010.99Dno D+−+−P(D | +) ≈ 16%

NCERT Class 12 Maths Chapter 13 Probability: what it teaches

Your teen uses conditional probability, the multiplication rule, independence, Bayes’ theorem, and random variables with probability distributions and mean.

Why it matters later. Probability underpins statistics, data science and risk analysis.

See it: this chapter in pictures

P(ace, then ace)= 4/52 × 3/51= 1/221
Conditional probability multiplies.
P(D|+) = P(+|D)P(D) / P(+)= 0.0095 / 0.059≈ 0.16
Base rates matter.
X = heads in 2 tossesP: 1/4, 1/2, 1/4 for 0, 1, 2mean = 1
Mean = Σ x P(x).

You need

  • cards and dice
  • a tree-diagram worksheet

Tonight’s 60 minutes

  1. Two cards drawn without replacement: P(both aces) (1/221).
  2. Check independence of two dice events.
  3. Bayes: a test is 95% accurate; disease rate 1%. P(disease | positive)? (about 16%)
  4. Find the mean of the number of heads in 2 coin tosses (1).

Words to use

  • conditional probability
  • independent
  • Bayes’ theorem
  • random variable
  • probability distribution
  • mean

Watch for

  • Confusing P(A|B) with P(B|A). Write which event is given before calculating.
  • Assuming independence without checking. Test P(A ∩ B) = P(A)P(B).

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

You95% accurate test, 1% disease. Positive means disease?

Your childOnly about 16% likely.

A game for this week: Bayes detective

  1. Set a scenario (test accuracy, base rate).
  2. Draw a tree diagram.
  3. Compute P(condition | positive).
  4. Discuss surprising results.

A 5-day plan, 60 minutes a day

  1. Day 1Explain-back.
  2. Day 2Worked examples.
  3. Day 3Practice set.
  4. Day 4Real-life problem.
  5. Day 5Mixed quiz.

Everyday moments to practise

  • Medical testing.
  • Spam filters.
  • Insurance.
  • Quality control.

Quick check

Ask these at the end of the week. Tap to see the answer.

P(both aces, no replacement)?

1/221.

Mean heads in 2 tosses?

1.

If A, B independent, P(A ∩ B)?

P(A)P(B).

Ready for the next chapter when your child…

  • Computes conditional probabilities.
  • Applies Bayes’ theorem.
  • Finds means of random variables.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Mathematics (Class 12). See the full Class 12 parent guide for every chapter.

Questions parents ask

What is conditional probability?

The probability of A given that B has occurred: P(A ∩ B)/P(B).

Why do positive tests mislead with rare diseases?

False positives from the large healthy group can outnumber true positives.

Is the binomial distribution included?

Check the current syllabus; it may be reduced.