JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Probability

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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 ____.

Answer: 28

Solution

Let the units function with probabilities

0.9

and

0.8

independently. The instrument fails when at least one unit fails:

P (fail) = 1 - 0.9 \times 0.8 = 0.28

. The event that only the first fails while the second works has probability

(1 - 0.9) \times 0.8 = 0.08

. Hence

p = \frac{0.08}{0.28} = \frac{2}{7}

, and

98 p = 98 \times \frac{2}{7} = 28

JEE Main · 2021 · 31 Aug 2021 · Shift 1 · Integer answer

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