A bag contains 3 green marbles and 6 blue marbles. What is the probability of drawing a blue marble, then another blue marble, then a green marble, replacing the marble after each draw?
Well, adding all the marbles together, 3 green marbles and 6 blue marbles, you would get 9 marbles in the bag altogether. If you place the marble back into the bag after drawing it, the probability of getting a green marble would be 3/9, or 1/3 of the bag. If you wanted to get a blue marble, your chances of getting it would be 6/9, or simplified, 2/3. I hope that helps :)
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To find the probability of drawing a blue marble, then another blue marble, then a green marble (with replacement after each draw), we need to multiply the probabilities of each event.
The probability of drawing a blue marble is 6/9, since there are 6 blue marbles out of a total of 9 marbles.
When we replace the marble after each draw, the probability remains the same for each draw.
So, the probability of drawing a blue marble, then another blue marble is (6/9) * (6/9) = 36/81.
The probability of drawing a green marble is 3/9, since there are 3 green marbles out of a total of 9 marbles.
So, the final probability of drawing a blue marble, then another blue marble, then a green marble is (36/81) * (3/9) = 108/729.
Simplifying, we get 4/27 as the probability.
To find the probability of drawing a blue marble, then another blue marble, then a green marble with replacement after each draw, we need to calculate the individual probabilities of each draw and then multiply them together.
Let's break it down step by step:
Step 1: Probability of drawing a blue marble
In this case, there are a total of 9 marbles in the bag, out of which 6 are blue. So, the probability of drawing a blue marble on the first draw is 6/9.
Step 2: Probability of drawing another blue marble
Since we replace the marble after each draw, the probability of drawing a blue marble again remains the same. Therefore, the probability of drawing another blue marble is also 6/9.
Step 3: Probability of drawing a green marble
After the first two draws, there are 9 marbles in the bag, but now 3 of them are green. So, the probability of drawing a green marble is 3/9.
Now, to find the overall probability, we multiply the individual probabilities together:
Probability = (6/9) * (6/9) * (3/9) = 108/729 = 0.148 (rounded to three decimal places)
So, the probability of drawing a blue marble, then another blue marble, then a green marble (with replacement after each draw) is approximately 0.148 or 14.8%.