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Probability question

2025 · Shift 2 · Q27

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PYQ Library
JEE Advanced
Mathematics
Probability
2025 · Shift 2 · Q27

Probability question

2025 · Shift 2 · Q27

JEE AdvancedMathematicsProbabilityNumerical+4 / −1

A factory has a total of three manufacturing units,

M_1, M_2

, and

M_3

, which produce bulbs independent of each other. The units

M_1, M_2

, and

M_3

produce bulbs in the proportions of

2: 2: 1

, respectively. It is known that

20 \%

of the bulbs produced in the factory are defective. It is also known that, of all the bulbs produced by

M_1, 15 \%

are defective. Suppose that, if a randomly chosen bulb produced in the factory is found to be defective, the probability that it was produced by

M_2

is

\frac{2}{5}

. If a bulb is chosen randomly from the bulbs produced by

M_3

, then the probability that it is defective is

\underline{\hspace{2cm}}

.

Numerical answer

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