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14. probability — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS14. probability1 Mark
MCQ
An ordinary cube has four blank faces, one face marked $2$ another marked $3$. Then the probability of obtaining a total of exactly $12$ in $5$ throws, is
  • A
    $\frac{5}{{1296}}$
  • B
    $\frac{5}{{1944}}$
  • ✓
    $\frac{5}{{2592}}$
  • D
    None of these
✓

Answer

Correct option: C.
$\frac{5}{{2592}}$
c
(c) $n = $ Total number of ways $ = {6^5}$

$A$ total of $12$ in $5$ throw can be obtained in following two ways -

$(i)$ One blank and four $3's = {}^5{C_1} = 5$

or $(ii)$ Three $2's$ and two $3's = {}^5{C_2} = 10$

Hence, the required probability $ = \frac{{15}}{{{6^5}}} = \frac{5}{{2592}}.$

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