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Question

The probability of the simultaneous occurrence of two events A and B is p. If the probability that exactly one of A,B occurs is q, then

  1. p open parentheses A to the power of ' end exponent close parentheses plus P open parentheses B to the power of ' end exponent close parentheses equals 2 plus 2 q minus p+PB'=2+2q-p'/>    
  2. P open parentheses A to the power of ' end exponent close parentheses plus P open parentheses B to the power of ' end exponent close parentheses equals 2 minus 2 p minus q+PB'=2-2p-q'/>    
  3. p left parenthesis A intersection B divided by A union B right parenthesis equals fraction numerator P over denominator p plus q end fraction    
  4. p open parentheses A to the power of ' end exponent intersection B close parentheses equals 1 minus p minus qB=1-p-q'/>    

The correct answer is: P open parentheses A to the power of ´ end exponent close parentheses plus P open parentheses B to the power of ´ end exponent close parentheses equals 2 minus 2 p minus q


    p open parentheses A intersection B close parentheses equals p text  and  end text P open parentheses A intersection stack B with minus on top close parentheses plus P open parentheses stack A with minus on top intersection B close parentheses equals q
    equals p open parentheses A union B close parentheses equals P plus q
    equals P open parentheses A close parentheses plus P open parentheses B close parentheses minus 2 P open parentheses A intersection B close parentheses equals q
    equals P open parentheses A close parentheses plus P open parentheses B close parentheses minus P open parentheses A intersection B close parentheses minus P open parentheses A intersection B close parentheses equals q
    equals P left parenthesis A union B right parenthesis minus P left parenthesis A intersection B right parenthesis equals q
    equals P left parenthesis A union B right parenthesis equals p plus q

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