Management Aptitude Test 2016 Paper

Question : 88 of 200

Marks: +1, -0

A speaks truth in 75% of cases and B in 80% of cases. A and B agree in a statement. What if the probability that the statement is true?

Solution:

(a) Let

E_{1}

= Both speak truth

\;\;\;\;\;\;\;\;\;E_{2}

= Both speak false
and

\;\;\;\;\;

E= A and 8 agree in a statement
Given,

\;

P(A) =

75/100 = 3/4

and

\;\;\;\;\;

P(B) =

80/100 = 4/5

∴ P(

E_{1}

) =

3/4 × 4/5 = 3/5

, P(

E_{2}

) =

1/4 × 1/5 = 1/20

Clearly, P

(E/E_{1})

= 1 and

P(E/E_{2}) =1

(E_{1}/E) = {P(E_{1})P(E/E_{1})}/ {P(E_{1})P(E/E_{1}) + P(E_{2})P(E/E_{2})

{{3/5×1}}/{3/5 + 1/20 } = 3/5/{{12+1}/20}

3/5 × 20/13 = 12/13

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