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Probability & Counting (Foundations)

Core skills for this exam family.

Phase 2 · JEE

Probability & Counting: core idea

(nk)\binom{n}{k}.

Example problem: hint and answer

Fair coin: P(H)P(H)?

Hint: Equally likely. Answer: 1/2.

Practice (9 problems — type your answers)

  • 1. Fair die: P(6)P(6)?

  • 2. One red one blue marble equal likely: P(red)P(\text{red})?

  • 3. If P(A)=1/3P(A)=1/3, P(Ac)P(A^c)?

  • 4. Two fair coins: P(two heads)P(\text{two heads})?

  • 5. Die: P(even)P(\text{even})?

  • 6. Number of outcomes rolling two dice?

  • 7. P(∅)P(\emptyset)?

  • 8. P(Ω)P(\Omega)?

  • 9. Standard deck 5252: P(ace)P(\text{ace})?

Probability & Counting Practice Problems — Foundations