Compound Probability
Unique ID: 0770
Score: $1 / 10$
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Question
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A bag contains 8 red marbles, 3 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the exact probability that both marbles drawn will be blue?
Answer Attempt 1 out of 2
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Answer
Final Answer: \(\boxed{\frac{1}{26}}\)
Step 1 ：Calculate the total number of marbles in the bag: \( 8 + 3 + 2 = 13 \)
Step 2 ：Calculate the probability of drawing the first blue marble: \( \frac{3}{13} \)
Step 3 ：Calculate the probability of drawing the second blue marble, given that the first one was already drawn: \( \frac{2}{12} \)
Step 4 ：Calculate the compound probability of drawing two blue marbles: \( \frac{3}{13} \times \frac{2}{12} \)
Step 5 ：Simplify the compound probability: \( \frac{3}{13} \times \frac{1}{6} = \frac{1}{26} \)
Step 6 ：Final Answer: \(\boxed{\frac{1}{26}}\)
