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Probability & Counting (Standard)

Multi-step exam-style items.

Phase 2 · JEE

FoundationsStandardAdvanced

Probability & Counting: core idea

P(A∩B)=P(A)P(B∣A)P(A\cap B)=P(A)P(B|A).

Example problem: hint and answer

Two coins: P(exactly one head)P(\text{exactly one head})?

Hint: HT or TH. Answer: 1/2.

Practice (9 problems — type your answers)

  • 1. Die expected value?

  • 2. Binomial n=2n=2, p=1/2p=1/2: P(X=1)P(X=1)?

  • 3. Without replacement: 2 red of 5, draw 1: P(red)P(\text{red})?

  • 4. Independent P(A)=0.4P(A)=0.4, P(B)=0.5P(B)=0.5: P(A∩B)P(A\cap B)?

  • 5. P(A∪B)P(A\cup B) if disjoint P(A)=0.2P(A)=0.2, P(B)=0.3P(B)=0.3?

  • 6. Bernoulli p=0.3p=0.3: variance?

  • 7. Choose 2 from 5: number of ways?

  • 8. At least one head in 2 flips: probability?

  • 9. Conditional: P(A)=0.5P(A)=0.5, P(A∩B)=0.2P(A\cap B)=0.2: P(B∣A)P(B|A)?

Probability & Counting Practice Problems — Standard