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A Speaks Truth in 75% of Cases and B in 80% of Cases. in What Percentage of Cases Are They Likely to Contradict Each Other, Narrating the Same Incident. - Mathematics

MCQ

A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident.

Options

  • `30/100`

  • `35/100`

  • `45/100`

  • `50/100`

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Solution

`35/100`

Explanation:
Let A = Event the A speaks the truth
B = Event that B speaks the truth

Then, `P(A)=75/100=3/4`

`P(B)=80/100=4/5`

`P(barA)=1-3/4=1/4`

`P(barB)=1-4/5=1/5`

Now, A and B contradict each other = [A lies and B true] or [A true and B lies]
∴ Required probability = `P(A).P(barB)+P(barA).P(B)`

= `(3/4xx1/5)+(1/4xx4/5)=7/20`

= `(7/20xx100)=35%or 35/100`

Concept: Probability (Entrance Exam)
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