Maths-
General
Easy

Question

If P space open parentheses A union B close parentheses equals 3 over 4 and P space open parentheses A with ‾ on top close parentheses equals 2 over 3, then P space open parentheses A with ‾ on top intersection B close parentheses equals

  1. 5/12    
  2. 7/12    
  3. fraction numerator 1 over denominator 12 end fraction    
  4. 1/2    

hintHint:

A with ‾ on top intersection B space a n d space A space a r e space m u t u a l l y space e x c l u s i v e space e v e n t s.

The correct answer is: 5/12


    S i n c e space space space space A with ‾ on top intersection B space a n d space A space a r e space m u t u a l l y space e x c l u s i v e space e v e n t s.
    P left parenthesis A right parenthesis space equals space 1 minus space P space open parentheses A with ‾ on top close parentheses
    P left parenthesis A right parenthesis space equals space 1 space minus space 2 over 3 space equals space 1 third
    left square bracket space P space open parentheses A with ‾ on top intersection B close parentheses space equals space P left parenthesis B right parenthesis space equals space P left parenthesis space A intersection B right parenthesis space right square bracket space...... space left parenthesis 1 right parenthesis
    Also, we know that
    P left parenthesis A union B right parenthesis space equals space P left parenthesis A right parenthesis space plus space P left parenthesis B right parenthesis space minus P left parenthesis A intersection B right parenthesis
    From (1)
    P left parenthesis A union B right parenthesis space equals space P left parenthesis A right parenthesis space plus space P space open parentheses A with ‾ on top intersection B close parentheses
    P left parenthesis A union B right parenthesis space equals space 1 third space plus space P space open parentheses A with ‾ on top intersection B close parentheses
    P space open parentheses A with ‾ on top intersection B close parentheses space equals space 3 over 4 minus space 1 third space equals space 5 over 12

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