If a jar contains 3 red, 4 green, and 5 blue marbles, what is the probability of drawing a green marble, then a blue marble, with replacement?

Instruction: Calculate the probability with replacement.

Context: This question evaluates the candidate's understanding of probabilities involving independent events with replacement.

Updated

Official answer

There are 12 marbles. A uniform first draw is green with probability 4/12. Replace it and mix before an independent second draw, which is blue with probability 5/12.

Therefore P(green then blue) = (4/12)(5/12) = 5/36, about 13.89%.

The order is specified. If either green/blue or blue/green were accepted, the two disjoint cases would total 10/36 = 5/18. Replacement keeps the counts fixed; the independent uniform-draw assumption supplies the multiplication of marginals.

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