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Probability: Basic formula sheet

Every formula in the Probability: Basic chapter for JEE Main, with one line on when it applies. Topic 1 is open to everyone; sign in free to read all 16 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.

Sample space and events

Classical probability
6× asked, last 2026
P(E)=n(E)n(S),0≤P(E)≤1P(∅)=0, P(S)=1\begin{aligned}&P(E)=\frac{n(E)}{n(S)},\qquad 0\le P(E)\le1\\&P(\emptyset)=0,\ P(S)=1\end{aligned}
Equally likely outcomes only. Count EE and SS the same way (both ordered or both unordered).
Unequal outcomes
5× asked, last 2024
P(A)=∑ω∈AP(ω),∑ω∈SP(ω)=1P(A)=\sum_{\omega\in A}P(\omega),\qquad \sum_{\omega\in S}P(\omega)=1
Biased coin or die: add weights; fix the unknown from total = 1. Head twice as likely: P(H)=2/3P(H)=2/3.
Complement, exclusive, odds
2× asked, last 2023
P(A′)=1−P(A)A∩B=∅⇒P(A∪B)=P(A)+P(B)\begin{aligned}&P(A^\prime)=1-P(A)\\&A\cap B=\emptyset\Rightarrow P(A\cup B)=P(A)+P(B)\end{aligned}
Odds a:ba:b in favour: P=a/(a+b)P=a/(a+b). Exclusive events also need ∑P(Ei)≤1\sum P(E_i)\le1.

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Practise Probability: Basic

13 more formulas in 5 topics

Addition theorem; Dice, coins and cards; Counting favourable cases; Equations, matrices and regions; and Independent trials. Read the first part free. Sign in free with Google to read the rest and download the PDF.

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Addition theorem

  • Two events3×
  • Three events3×

Dice, coins and cards

  • Dice6×
  • Coins3×

Counting favourable cases

  • Divisibility9×
  • A.P. triples3×
  • Arrangements4×
  • Drawing without replacement4×
  • Random maps and boxes6×

Equations, matrices and regions

  • Random quadratic6×
  • Random matrices6×
  • Geometric probability5×

Independent trials

  • Independent trials11×

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About 80 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: Basic

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Version 1, October 2026. Free to share for study, as it is. Please don't sell it or remove the PrepWiser name.

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