A box has five same-sized balls: three green and two orange. Balls are drawn one at a time. Green balls are not replaced, while orange balls are replaced with another orange ball. After the first draw, what is the probability that the next ball is orange?
Condition on the first draw. With probability 3/5 it is green, leaving two orange among four balls, so the next-orange probability is 1/2. With probability 2/5 it is orange and replaced, leaving probability 2/5. Total=(3/5)(1/2)+(2/5)(2/5)=3/10+4/25=23/50, D.
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