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A company has two plants to manufacture televisions. Plant- I manufactures 70%
televisions and plant -II manufactures 30%. At plant -I, 80% of the televisions are rated as of standard quality and at plant -II, 90% of the televisions are rated as of standard quality. A television is chosen at random and is found to be standard quality. The probability that it has come from plant -II is

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$\frac{3}{5}$

$\frac{27}{83}$

$\frac{17}{50}$

$\frac{9}{83}$

answer is B.

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Detailed Solution

Let E be the event that a television chosen randomly is of standard quality. We have to find

$P (II / E) = \frac{P (E / II) . p (II)}{P (E / I) . P (I) + P (E / II) . P (II)} = \frac{(9 / 10) (3 / 10)}{(4 / 5) (7 / 10) + (9 / 10) (3 / 10)} = 27 / 83$

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