# 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

#### 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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