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Person "A" says the truth $60 \%$ of the time, and person "B" does so $90 \%$ of the time. In what percentage of cases are they likely to contradict each other in stating the same fact?

  1. $6 \%$
  2. $36 \%$
  3. $42 \%$
  4. $54 \%$
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when they both say true the probability is $60 \times \frac{90}{100} = 54;$
when the both say false at same time is $40 \times \frac{10}{100}=4;$
so the say always the same fact is $54+4=58 \%;$
so the percentage of cases that they contradict each other is $100-58=42 \%$
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