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14. probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS14. probability1 Mark
MCQ
Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2}, \frac{3}{4}, \frac{1}{4}, \frac{1}{8}$. Then the probability that the problem is solved correctly by at least one of them is
  • ✓
    $\frac{235}{256}$
  • B
    $\frac{21}{256}$
  • C
    $\frac{3}{256}$
  • D
    $\frac{253}{256}$
✓

Answer

Correct option: A.
$\frac{235}{256}$
a
$P \text { (problem solved by at least one) }=1- P \text { (problem is not solved by by all) } $

$=1- P (\overline{ A }) P (\overline{ B }) P (\overline{ C }) P (\overline{ D }) $

$=1-\left(\frac{1}{2}\right)\left(\frac{1}{4}\right)\left(\frac{3}{4}\right)\left(\frac{7}{8}\right)=1-\frac{21}{256}=\frac{235}{256}$

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