Compound Probability
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Question
A bag contains 2 red marbles, 3 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1oth of a percent, that both marbles drawn will be red?
Answer Attempt 2 out of 2
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Step 1 ：To find the probability that both marbles drawn will be red, we need to calculate the probability of drawing a red marble on the first draw and then multiply it by the probability of drawing a red marble on the second draw, given that the first marble drawn was red.

Step 2 ：The total number of marbles in the bag is 10.

Step 3 ：The probability of drawing a red marble on the first draw is \(\frac{2}{10} = 0.2\).

Step 4 ：Given that the first marble drawn was red, there is now 1 red marble left and a total of 9 marbles in the bag. So, the probability of drawing a red marble on the second draw is \(\frac{1}{9} \approx 0.1111111111111111\).

Step 5 ：The probability of both marbles drawn being red is \(0.2 \times 0.1111111111111111 = 0.022222222222222223\).

Step 6 ：Rounded to the nearest 10th of a percent, the probability is \(0.022 \times 100 = 2.2\%\).

Step 7 ：Final Answer: \(\boxed{0.022}\)