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  • 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 and that of the s

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 p$, then $98 \mathrm{p} is equal to________.
 

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best_answer

P (First unit is functional)
= P\left ( F \right )= 0\cdot 9\Rightarrow P\left ( \bar{F} \right )= 0\cdot 1
P (Second unit is functional)
= P\left ( S \right )= 0\cdot 8\Rightarrow P\left ( \bar{S} \right )= 0\cdot 2
Desired Probabolity
P= \frac{P\left ( \bar{F} \right )P\left ( S \right )}{P\left ( \bar{F} \right )P\left ( S \right )+P\left ( \bar{S} \right )P\left ( F \right )+P\left ( \bar{S} \right )P\left ( \bar{F} \right )}
   = \frac{0\cdot 1\times 0\cdot 8}{0\cdot 1\times 0\cdot 8+0\cdot 2\times 0\cdot 9+0\cdot 1\times 0\cdot 2}
   = \frac{8}{8+18+2}= \frac{8}{28}= \frac{2}{7}
So 98P= \frac{2}{7}\times 98= 28

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Deependra Verma

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