Consider two events E₁ and E₂ such that probability of E₁, Pr[E₁] = 1/2,…

GATE · 1999 · CS · Question 2 subparts

Consider two events E₁ and E₂ such that probability of E₁, Pr[E₁] = 1/2, probability of E₂, Pr[E₂] = 1/3, and probability of E₁ and E₂, Pr[E₁ and E₂] = 1/5. Which of the following statements is/are true?

  1. A.

    Pr[E₁ or E₂] is 2/3

  2. B.

    Events E₁ and E₂ are independent.

  3. C.

    Events E₁ and E₂ are not independent.

  4. D.

    P(E₁ | E₂) = 4/5

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