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13. probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths13. probability1 Mark
MCQ
A six faced fair dice is thrown until $2$ comes, then the probability that $2$ comes in even number of trials is (dice having six faces numbered $1, 2, 3, 4, 5$ and $6$)
  • A
    $\frac {1}{6}$
  • B
    $\frac {5}{6}$
  • C
    $\frac {6}{11}$
  • ✓
    $\frac {5}{11}$
✓

Answer

Correct option: D.
$\frac {5}{11}$
d
$P(z)=\frac{1}{6} \quad P(\bar{z})=\frac{5}{6}$

$\therefore \quad \mathrm{P}(2 \text { comes in even trial })$

${=\mathrm{P}(\bar{z} \mathrm{z} \text { or } \bar{z} \bar{z} \bar{z} z \text { or } \ldots \ldots \ldots \infty)} $

${=\frac{5}{6} \times \frac{1}{6}+\left(\frac{5}{6}\right)^{3} \cdot \frac{1}{6}+\ldots \ldots \infty} $

${=\frac{5}{6} \times \frac{1}{6}} $

${=\frac{\frac{5}{6} \times \frac{1}{6}}{1-\left(\frac{5}{6}\right)^{2}}=\frac{5}{11}}$

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