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Probability — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsProbability2 Marks
MCQ
The probability that A speaks truth is $\frac{4}{5}$, while this probability for $B$ is $\frac{3}{4}$. The probability that they contradict each other when asked to speak on a fact
  • A
    $\frac{4}{5}$
  • B
    $\frac{1}{5}$
  • ✓
    $\frac{7}{20}$
  • D
    $\frac{3}{20}$
✓

Answer

Correct option: C.
$\frac{7}{20}$
(C)
Here, $P ( A )=\frac{3}{4}, P ( B )=\frac{4}{5}$
$\therefore P (\overline{ A })=\frac{1}{4}$ and $P (\overline{ B })=\frac{1}{5}$
$\therefore $ Required probability
$= P (A) \cdot P (\overline{ B }) +\, P (\bar{A}) \cdot P ( B )=\frac{7}{20}.$

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