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STD 11 - 14. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. probability4 Marks
MCQ
In a regular $15$ -sided polygon with all its diagonals drawn, a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is
  • ✓
    $\frac{2}{3}$
  • B
    $\frac{5}{6}$
  • C
    $\frac{8}{9}$
  • D
    $\frac{8}{9}$
✓

Answer

Correct option: A.
$\frac{2}{3}$
a
(a)

Total number of diagonals of $15$ sided polygons

$={ }^{15} C_2-15=\frac{15 \times 14}{2}-15=90$

$\therefore$ Number of total shortest digonals $=15$

And number of longest digonals $=15$

$\therefore$ 'he probability that the selected diagonal is neither shortest nor longest

$=\frac{90-30}{90}=\frac{60}{90}=\frac{2}{3}$

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