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14. probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS14. probability1 Mark
MCQ
A multiple choice examination has $5$ questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get $4$ or more correct answers just by guessing is :
  • A
    $\frac{{17}}{{{3^5}}}$
  • B
    $\;\frac{{13}}{{{3^5}}}$
  • ✓
    $\;\frac{{11}}{{{3^5}}}$
  • D
    $\;\frac{{10}}{{{3^5}}}$
✓

Answer

Correct option: C.
$\;\frac{{11}}{{{3^5}}}$
c
$p=\frac{1}{3}, q=\frac{2}{3}$

$^{5} \mathrm{C}_{4}\left(\frac{1}{3}\right)^{4} \cdot \frac{2}{3}+^{5} \mathrm{C}_{5}\left(\frac{1}{3}\right)^{5}$

$=5 \cdot \frac{2}{3^{5}}+\frac{1}{3^{5}}=\frac{11}{3^{5}}$

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