JEE MAIN - Mathematics (2021 - 31st August Morning Shift - No. 24)
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
Explanation
I1 = first unit is functioning
I2 = second unit is functioning
P(I1) = 0.9, P(I2) = 0.8
P($$\overline {{I_1}} $$) = 0.1, P($$\overline {{I_2}} $$) = 0.2
$$P = {{0.8 \times 0.1} \over {0.1 \times 0.2 + 0.9 \times 0.2 + 0.1 \times 0.8}} = {8 \over {28}}$$
$$98P = {8 \over {28}} \times 98 = 28$$
I2 = second unit is functioning
P(I1) = 0.9, P(I2) = 0.8
P($$\overline {{I_1}} $$) = 0.1, P($$\overline {{I_2}} $$) = 0.2
$$P = {{0.8 \times 0.1} \over {0.1 \times 0.2 + 0.9 \times 0.2 + 0.1 \times 0.8}} = {8 \over {28}}$$
$$98P = {8 \over {28}} \times 98 = 28$$
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