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AP EAMCET2009MathematicsProbability

Suppose that E₁ and E₂ are two events of a random experiment such that P (E₁ )= 1 4 , P (E₂ / E₁ )= 1 2 and P (E₁ / E₂ )= 1 4 , observe the lists given below The correct matching of the List I from the List II is (A) (B) (C) (D)

Options

  1. A(ii) (iii) (vi) (i)
  2. B(iv) (v) (vi) (i)
  3. C(iv) (ii) (vi) (i)
  4. D(i) (ii) (iii) (iv)

Correct answer

C. (iv) (ii) (vi) (i)

Step-by-step solution

(A) Given, P (E₁ )= 1 4 , P ( E₁ E₂ )= 1 4 and P ( E₂ E₁ )= 1 2 array ll & P (E₂ E₁ ) P (E₁ ) = 1 2 & P (E₂ E₁ )= 1 8 Also, & P ( E₁ E₂ )= 1 4 & P (E₁ E₂ ) P (E₂ ) = 1 4 & 1 8 P (E₂ ) = 1 4 & P (E₂ )= 1 2 array aligned (B) P (E₁ E₂ ) & =P (E₁ )+P (E₂ )-P (E₁ E₂ ) & = 1 4 + 1 2 - 1 8 = 5 8 aligned aligned (C) P ( E ₁ E ₂ ) & = P ( E ₁ E ₂ ) P ( E ₂ ) & = 1-P (E₁ E₂ ) 1-P (E₂ ) = 1- 5 8 1- 1 2 & = 3 4 aligned aligned (D) P ( E₁ E ₂ ) & = P (E₁ E ₂ ) P ( E ₂ ) & = P (E₁ )-P (E₁ E₂ ) 1-P (E₂ ) & = 1 4 - 1 8 1- 1 2 = 1

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