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?

Initially, the box contains $3$ green balls and $2$ orange balls, making a total of $5$ balls.

We calculate the probability of drawing an orange ball in the second draw ($O_2$) using the Law of Total Probability:

Case 1: First ball drawn is green ($G_1$)

• Probability of drawing a green ball first: $P(G_1) = \frac{3}{5}$.

• Since green balls are not replaced, the box now contains $2$ green balls and $2$ orange balls (total $4$ balls).

• Conditional probability of drawing an orange ball second: $P(O_2 \mid G_1) = \frac{2}{4} = \frac{1}{2}$.

Case 2: First ball drawn is orange ($O_1$)

• Probability of drawing an orange ball first: $P(O_1) = \frac{2}{5}$.

• Since orange balls are replaced, the box still contains $3$ green balls and $2$ orange balls (total $5$ balls).

• Conditional probability of drawing an orange ball second: $P(O_2 \mid O_1) = \frac{2}{5}$.

Total Probability:

Hence, the correct option is (D).