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GATE CSE 2022 Q8: Probability of orange on the second draw with partial replacement

Question

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn from the box one at a time. If a green ball is drawn, it is not replaced. If an orange ball is drawn, it is replaced with another orange ball.

First ball is drawn. What is the probability of getting an orange ball in the next draw?

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Answer: D (official GATE 2022 final answer key)

Concept used: Total probability: condition on the colour of the first ball.

First step: First green (35\frac{3}{5}) leaves 2 green and 2 orange; first orange (25\frac{2}{5}) leaves the box unchanged. Add 35⋅24+25⋅25\frac{3}{5} \cdot \frac{2}{4} + \frac{2}{5} \cdot \frac{2}{5}.

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Source: official GATE 2022 CS question paper and final answer key, organised by IIT Kharagpur. Question paper · Answer key

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