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GATE 2022 CS – Question 8

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

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?

  1. $\frac{1}{2}$
  2. $\frac{8}{25}$
  3. $\frac{19}{50}$
  4. $\frac{23}{50}$

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Correct answer: (D) $\frac{23}{50}$

Explanation

If the first ball is green (3/5), the box has 2 green and 2 orange, so P(orange)=1/2. If the first ball is orange (2/5), the box is unchanged, so P(orange)=2/5. Total $=\frac35\cdot\frac12+\frac25\cdot\frac25=\frac{23}{50}$.