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? A. 1/3 B. 2/5 C. 23/50 D. 11/30

GATE 2022 · General Aptitude · Probability · medium

Answer: P(orange ball on the second draw) = (3/5)*(1/2) + (2/5)*(2/5) = 15/50 + 8/50 = 23/50.

1. First draw probabilities: P(first = green) = 3/5. P(first = orange) = 2/5.
2. Second draw given first was green: Green removed, not replaced: box now has 2G + 2O = 4 balls. P(orange | first green) = 2/4 = 1/2.
3. Second draw given first was orange: Orange replaced by orange: box stays 3G + 2O = 5 balls. P(orange | first orange) = 2/5.
4. Apply law of total probability: P(orange second) = (3/5)*(1/2) + (2/5)*(2/5) = 3/10 + 4/25. Converting: 3/10 = 15/50, 4/25 = 8/50. Sum = 23/50.