Question

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

A) 30/100 B) 35/100 C) 45/100 D) 50/100

Answer 1

Answer:

B) 35/100

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Step-by-step explanation:

A = Event that A speaks the truth

A = Event that A speaks the truthB = Event that B speaks the truth

A = Event that A speaks the truthB = Event that B speaks the truth Then P(A) = 75/100 = 3/4

A = Event that A speaks the truthB = Event that B speaks the truth Then P(A) = 75/100 = 3/4P(B) = 80/100 = 4/5

= 4/5P(A-lie) = 1−34= 1/4

= 4/5P(A-lie) = 1−34= 1/4 P(B-lie) = 1−45= 1/5

= 4/5P(A-lie) = 1−34= 1/4 P(B-lie) = 1−45= 1/5

= 4/5P(A-lie) = 1−34= 1/4 P(B-lie) = 1−45= 1/5 Now, A and B contradict each other =[A lies and B true] or [B true and B lies]

= 4/5P(A-lie) = 1−34= 1/4 P(B-lie) = 1−45= 1/5 Now, A and B contradict each other =[A lies and B true] or [B true and B lies] = P(A).P(B-lie) + P(A-lie).P(B)

= 4/5P(A-lie) = 1−34= 1/4 P(B-lie) = 1−45= 1/5 Now, A and B contradict each other =[A lies and B true] or [B true and B lies] = P(A).P(B-lie) + P(A-lie).P(B) = (35*15)+(14*45)=720

= 4/5P(A-lie) = 1−34= 1/4 P(B-lie) = 1−45= 1/5 Now, A and B contradict each other =[A lies and B true] or [B true and B lies] = P(A).P(B-lie) + P(A-lie).P(B) = (35*15)+(14*45)=720 = (720*100)= 35%