The probability that A speaks truth is $75 \%$ and the probability that B speaks truth is $80 \%$. The…

The probability that A speaks truth is $75 \%$ and the probability that B speaks truth is $80 \%$. The probability that they contradict each other when asked to speak on a fact is
  1. $\frac{3}{20}$
  2. $\frac{4}{20}$
  3. $\frac{7}{20}$
  4. $\frac{5}{20}$

Solution

$P(A)=\frac{75}{100}, P(\bar{A})=\frac{25}{100}$ $\begin{aligned} & P(B)=\frac{80}{100}, P(\bar{B})=\frac{20}{100} \\ & \begin{aligned} P(\text { contradict }) & =P(A \cap \bar{B})+P(\bar{A} \cap B) \\ & =\frac{75}{100} \times \frac{20}{100}+\frac{80}{100} \times \frac{25}{100}=\frac{7}{20}\end{aligned}\end{aligned}$

Asked in: AP EAMCET 2024 (23 May Shift 1)

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