Verified Solution • 2025–26 Session moderate

QJEEM21Mada9d: JEE Main 2021 Mathematics - Class 12 JEEM21Mada9d Solution: An electric instrument consists of two units. Each unit must…

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 _____________.

Step-by-Step Verified Solution

I1 = first unit is functioning

I2 = second unit is functioning

P(I1) = 0.9, P(I2) = 0.8

P( I1‾\overline {{I_1}} ) = 0.1, P( I2‾\overline {{I_2}} ) = 0.2

P=0.8×0.10.1×0.2+0.9×0.2+0.1×0.8=828P = {{0.8 \times 0.1} \over {0.1 \times 0.2 + 0.9 \times 0.2 + 0.1 \times 0.8}} = {8 \over {28}}

98P=828×98=2898P = {8 \over {28}} \times 98 = 28

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