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13. probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths13. probability1 Mark
MCQ
An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is $0.9$ and that of the second unit is $0.8$. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is $\mathrm{p}$, then $98\, \mathrm{p}$ is equal to ..... .
  • A
    $14$
  • B
    $16$
  • C
    $48$
  • ✓
    $28$
✓

Answer

Correct option: D.
$28$
d
$\mathrm{I}_{1}=$ first unit is functioning

$\mathrm{I}_{2}=$ second unit is functioning

$\mathrm{P}\left(\mathrm{I}_{1}\right)=0.9, \mathrm{P}\left(\mathrm{I}_{2}\right)=0.8$

$\mathrm{P}\left(\overline{\mathrm{I}}_{1}\right)=0.1, \mathrm{P}\left(\overline{\mathrm{I}}_{2}\right)=0.2$

$\mathrm{P}=\frac{0.8 \times 0.1}{0.1 \times 0.2+0.9 \times 0.2+0.1 \times 0.8}=\frac{8}{28}$

$98 \mathrm{P}=\frac{8}{28} \times 98=28$

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