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AP EAMCET202420 May 2024Morning ShiftMathematicsProbabilityActual

A , B , C are mutually exclusive and exhaustive events of a random experiment and E is an event that occurs in conjunction with one of the events A , B , C . The conditional Probabilities of E given the happening of A , B , C are respectively 0.6,0.3 and 0.1 . If P ( A )=0.30 and P ( B )= 0.50 , then P(C E)=

Options

  1. A2 35
  2. B15 35
  3. C18 35
  4. D17 35

Correct answer

A. 2 35

Step-by-step solution

P( ~A )=0.30, P( ~B )=0.50 Since A , B , C are mutually exclusive and exhaustive P(A)+P(B)+P(C)=1 P ( C )=0.20, P(E / A)=0.6, P(E / B)=0.3, P(E / C)=0.1 Now, P(C / E)= P(C) P(E / C) P(A) P(E / A)+P(B) P(E / B)+P(C) P(E / C) = 0.2 0.1 (0.3)(0.6)+(0.5)(0.3)+(0.2)(0.1) = 0.02 0.35 = 2 35

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