A speaks truth in 75% of cases and B in 80% of cases. In what percentage of case

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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
Options
A. 30/100
B. 35/100
C. 45/100
D. 50/100

Correct Answer

35/100

Explanation

Let A = Event that 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(A-lie) = $1 - \frac{3}{4}$ = 1/4

P(B-lie) = $1 - \frac{4}{5}$ = 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)

= $(\frac{3}{5} * \frac{1}{5}) + (\frac{1}{4} * \frac{4}{5}) = \frac{7}{20}$

= $(\frac{7}{20} * 100)$ = 35%