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COMEDK2023MathematicsProbability

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B)= 3 2 P(A) and P(C)= 1 2 P(B) , then P(A C) equals to

Options

  1. A10 13
  2. B3 13
  3. C6 13
  4. D7 13

Correct answer

D. 7 13

Step-by-step solution

Given, P(B)= 3 2 P(A) and P(C)= 1 2 P(B) Since, A, B and C are mutually exclusive and exhaustive events. array ll & P(A)+P(B)+P(C)=1 & P(A)+ 3 2 P(A)+ 1 2 3 2 P(A)=1 & P(A) (1+ 3 2 + 3 4 )=1 & P(A) ( 13 4 )=1 P(A)= 4 13 & P(C)= 1 2 3 2 P(A)= 3 4 4 13 = 3 13 array Also, A, B and C are mutually exclusive. aligned & (A B)=P(B C)=P(C A)=0 & Now, P(A C)=P(A)+P(C)-P(A C) & = 4 13 + 3 13 -0= 7 13 aligned

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