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Answer :
Final answer:
The probability that both marbles drawn one after the other with replacement from a bag containing 12 red and 8 black marbles are red is 9/25.
Explanation:
The question you've posed pertains to the probability of drawing two red marbles from a bag, one after the other, with replacement. Since there are 12 red marbles and 8 black marbles, the total number of marbles in the bag is 20. The probability of drawing a red marble in one draw is 12/20 or 3/5.
Since the marble is replaced after the first draw, the same probabilities apply to the second draw. To find the probability of two independent events both happening, we multiply the probabilities of each event occurring separately. Thus, the probability of drawing the first red marble is 3/5, and the probability of drawing a second red marble is also 3/5.
The overall probability of drawing two red marbles in a row with replacement is therefore (3/5) × (3/5) = 9/25.
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