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08/02/2022 3:15 pm
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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 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 p is equal to _________.
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08/02/2022 3:20 pm
I1 = first unit is functioning
I2 = second unit is functioning
P(I1) = 0.9, P(I2) = 0.8
\(P(\bar I_1)\) = 0.1, \(P(\bar I_2)\) = 0.2
P = \(\frac{0.8 \times 0.1}{0.1 \times 0.2 + 0.9 \times 0.2 + 0.1 \times 0.8}\)
= \(\frac{8}{28}\)
98P = \(\frac{8}{28}\) x 98 = 28