GATE2014 EC-3: GA-10

Question

A batch of one hundred bulbs is inspected by testing four randomly chosen bulbs. The batch is rejected if even one of the bulbs is defective. A batch typically has five defective bulbs. The probability that the current batch is accepted is__________.

Answer 1

In a batch there are total $100$ bulbs of which
$95$ are working
$5$ are defective.

$P$(Selecting $4$ working bulbs)$ = \dfrac{95}{100}\times \dfrac{94}{99}\times \dfrac{93}{98}\times \dfrac{92}{97}= 0.81$

Comments

by default is without replacement

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Hi @rajan,

Actually we are choosing in one go ->

So P(Selecting 4 working bulbs) = $\frac{\binom{95}{4}}{\binom{100}{4}}$

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In selected answer bulbs are selected one by one ..but it is not given

we should take P(Selecting 4 working bulbs out of 100) = $\binom{95}{4} / \binom{100}{4}$

Answer 2

Apologies, please bear with the wrong orientation.