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Probability: Advanced formula sheet

Every formula in the Probability: Advanced chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 17 and download the PDF.

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How we count: 7× asked means 7 past JEE Main questions in the PrepWiser bank needed that formula, and "last" is the latest year one appeared. ★ marks formulas asked 8 or more times.

Conditional probability

Conditional probability
7× asked, last 2025
P(A∣B)=P(A∩B)P(B)P(A∩B)=P(B) P(A∣B)=P(A) P(B∣A)\begin{aligned}&P(A\mid B)=\frac{P(A\cap B)}{P(B)}\\&P(A\cap B)=P(B)\,P(A\mid B)=P(A)\,P(B\mid A)\end{aligned}
P(B)>0P(B)>0; BB is the new sample space. Two dice, sum a multiple of 4: 9 outcomes, one shows a 4, so 1/91/9.
Complements inside a condition
3× asked, last 2022
P(A∣B′)=P(A)−P(A∩B)1−P(B)P(A\mid B^{\prime})=\frac{P(A)-P(A\cap B)}{1-P(B)}
Complement the event, never the condition: P(A′∣B)=1−P(A∣B)P(A^{\prime}\mid B)=1-P(A\mid B).
Multiplication theorem
2× asked, last 2025
P(A∩B∩C)=P(A) P(B∣A) P(C∣A∩B)P(A\cap B\cap C)=P(A)\,P(B\mid A)\,P(C\mid A\cap B)
Time order. Without replacement the kk-th draw has the first draw’s chance. 4 W, 6 B: P(1st B∣2nd B)=5/9P(\text{1st B}\mid\text{2nd B})=5/9.

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Practise Probability: Advanced

14 more formulas in 3 topics

Independent events and repeated trials, Total probability and Bayes and Random variables and distributions. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Independent events and repeated trials

  • Independent events4×
  • Pairwise vs mutual3×
  • Waiting for the first success3×

Total probability and Bayes

  • Total probability2×
  • Transfer, then draw2×
  • Bayes' theorem14×
  • Positive test
  • Unknown make-up, lost cards4×

Random variables and distributions

  • Probability distribution10×
  • Mean and variance7×
  • Linear change1×
  • Distributions from experiments5×
  • Sample without replacement7×
  • Binomial distribution23×

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About 95 past JEE Main questions from this chapter, with instant answer checking and step-by-step solutions where available. Free, and you can start without signing up.

Practise Probability: Advanced

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