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)
\frac{1}{2}
(B)
\frac{8}{25}
(C)
\frac{19}{50}
(D)
\frac{23}{50}
Answer: (D)
Explanation:
We have a box with 5 balls in total, three of which are green and two of which are orange. The chance of obtaining an orange ball in the second draw must be calculated. So, for the first ball drawn, there will be two scenarios. Green or orange might be used for the first ball.
Case 1: If the first ball drawn is green, we will only have four balls in the box instead of five if we get the orange ball in the second draw.
3/5 * 2/4 = 3/10
Case 2: If the first ball drawn is orange, we will be left with just 5 balls in the second draw since the orange ball will be replaced with a new orange ball.
2/5 * 25 = 4/25
Now, the probability of getting the orange ball in the 2nd draw will be
3/10 + 4/25 = (15+8)/50 = 23/50
Quiz of this Question
Please comment below if you find anything wrong in the above post