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Question: A jar of marbles is used to represent the chores that need to be done in the house. The jar contains 5 red marbles, 7 blue marbles, 3 green marbles, 4 black marbles, and 9 yellow marbles. Each marble represents a different chore: red represents vacuuming, blue represents cleaning the bathroom, green represents laundry, black represents dishes, and yellow represents mowing the lawn. A marble is drawn at random and then replaced before a second marble is drawn. What is the probability that both marbles were red? Express your answer as a decimal rounded to the nearest thousandth.
To find the probability of drawing two red marbles in a row with replacement, we can multiply the individual probabilities of drawing a red marble each time. First, let's find the probability of drawing a red marble: There are 5 red marbles, and a total of 5(red)+7(blue)+3(green)+4(black)+9(yellow)=28 marbles in the jar. So, the probability of drawing a red marble is: 5/28. Since the marble is replaced, the probability of drawing a red marble in the second draw remains the same, 5/28. Now, let's multiply the individual probabilities to find the probability of drawing two red marbles in a row: Probability = (5/28) * (5/28) = 25/784. To convert this into a decimal rounded to the nearest thousandth, we can divide the numerator by the denominator: 25 ÷ 784 ≈ 0.032. Therefore, the probability of drawing two red marbles in a row with replacement is approximately 0.032 or 3.2%.
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