AP EAMCET · Maths · Probability

$P$ speaks truth in $70 %$ of the cases and $Q$ in $80 %$ of the cases. In what percent of cases are they likely to agree in stating the same fact

A $38 %$
B $48 %$
C $52 %$
D $62 %$

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Answer & Solution

Correct Answer

(D) $62 %$

Step-by-step Solution

Detailed explanation

Let A and B denote the events P speaks the truth and Q speaks the truth respectively. Given P(A)=70100 and P(B)=80100 Hence, PA¯=1-P(A) and P(B¯)=1-PB ⇒PA¯=1-70100=30100 and PB¯=1-80100=20100. We have to find the probability that they agree in stating…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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P speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree in stating the same fact

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$P$ speaks truth in $70 %$ of the cases and $Q$ in $80 %$ of the cases. In what percent of cases are they likely to agree in stating the same fact