GATE 2017 EE (EE2) – Question 11

Engineering Mathematics · Probability and Statistics: Conditional probability · 1 mark · Multiple choice

An urn contains 5 red and 5 black balls. One ball is drawn randomly and discarded without observing its colour. The probability that a second random draw is red is

$1/2$
$4/9$
$5/9$
$6/9$

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Correct answer: (A) $1/2$

Explanation

Condition on the first draw. With probability 1/2 it was red, leaving 4 red out of 9; with probability 1/2 it was black, leaving 5 red out of 9.

Thus $P(R_2)=\tfrac12\tfrac49+\tfrac12\tfrac59=1/2$. Ignoring the unobserved first colour does not favour either colour in the second position. Hence **A**.

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