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A box contains three red marbles and six blue marbles. What is the probability of selecting at
random, without replacement, two blue marbles?
The Answers are:
1/9
5/12
1/12
4/9
First, find the total number of marbles in the box: 3 red + 6 blue = 9 total marbles.
Next, find the probability of selecting a blue marble on the first draw: 6 blue marbles / 9 total marbles = 2/3.
After selecting a blue marble on the first draw, there will be 5 blue marbles and 8 total marbles left.
Then, find the probability of selecting another blue marble on the second draw: 5 blue marbles / 8 total marbles = 5/8.
To find the overall probability of selecting two blue marbles without replacement, multiply the probabilities of each step: (2/3) * (5/8) = 10/24 = 5/12.
Therefore, the probability of selecting two blue marbles at random without replacement is 5/12.