A box contains five balls of same size and shape. Three of them are green…
2022
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.
1/2 - B.
8/25 - C.
19/50 - D.
23/50
Attempted by 84 students.
Show answer & explanation
Correct answer: D
Key idea: Use the law of total probability by considering the two possible outcomes of the first draw (green or orange).
If the first ball is green: probability = 3/5. After removing a green, there are 2 green and 2 orange left, so the probability of orange next = 2/4 = 1/2. Contribution = (3/5) * (1/2) = 3/10.
If the first ball is orange: probability = 2/5. An orange is replaced by another orange, so the composition stays 3 green and 2 orange, and the probability of orange next = 2/5. Contribution = (2/5) * (2/5) = 4/25.
Add the two contributions: 3/10 + 4/25 = 15/50 + 8/50 = 23/50.
Answer: 23/50.
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