Applied Course | Mock GATE | Test 1 | Question: 33

Question

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?

• A. $6 \%$
• B. $36 \%$
• C. $42 \%$
• D. $54 \%$

Answer 1

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 $100-58=42 \%$