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

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 14. probability4 Marks
MCQ
Let a computer program generate only the digits $0$ and $1$ to form a string of binary numbers with probability of occurrence of $0$ at even places be $\frac{1}{2}$ and probability of occurrence of $0$ at the odd place be $\frac{1}{3}$. Then the probability that $'10'$ is followed by $'01'$ is equal to :
  • A
    $\frac{1}{18}$
  • B
    $\frac{1}{3}$
  • C
    $\frac{1}{6}$
  • ✓
    $\frac{1}{9}$
✓

Answer

Correct option: D.
$\frac{1}{9}$
d
$\underset{\text { odd place }}{1} \underset{\text { even place }}{0} \underset{\text { odd place }}{0} \underset{\text { even place }}{1}$

$\underset{\text { even place }}{1} \underset{\text { odd place }}{0} \underset{\text { even place }}{0} \underset{\text { odd place }}{1}$

$\Rightarrow\left(\frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{2} \cdot \frac{2}{3}\right)+\left(\frac{2}{2} \cdot \frac{1}{2} \cdot \frac{1}{3} \cdot \frac{1}{2}\right)$

$\Rightarrow \, \frac{1}{9}$

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