Mystery of the Blue Marbles: A Mathematical Adventure
Intro:
Imagine you're standing in a bustling marketplace, captivated by the sights and sounds around you.
Suddenly, you stumble upon a peculiar stall overflowing with colorful marbles.
Three red, eight blue, and five green marbles to be exact! What mysteries lie within these vibrant spheres Let's embark on a mathematical journey to solve the riddle of the blue marbles!
The Challenge:
Two marbles are chosen at random from the bag.
What is the probability, to the nearest 1000th, that both marbles drawn will be blue
This is our challenge, a puzzle waiting to be solved!
Gathering Clues:
Before tackling this mathematical conundrum, we need to gather our clues.
We know the total number of marbles is 3 + 8 + 5 = 16. We also know the desired outcome: two blue marbles.
But how do we calculate the probability of this specific event occurring
Step 1: Probability of the First Marble:
The probability of drawing a blue marble in the first draw is 8/16, as there are 8 blue marbles and 16 marbles total.
However, after the first marble is drawn, we are left with 15 marbles and 7 blue marbles remaining.
Step 2: Probability of the Second Marble:
Now, the probability of drawing a blue marble for the second draw changes slightly. Since the first marble was removed, there are only 7 blue marbles remaining out of a total of 15 marbles.
Therefore, the probability of drawing another blue marble for the second draw is 7/15.
Combining the Clues:
To calculate the probability of both events happening consecutively (drawing a blue marble twice), we need to multiply the probabilities of each individual event.
This is because each event is independent of the other.
Therefore, the overall probability of drawing two blue marbles is:
Probability = (Probability of 1st Blue Marble) x (Probability of 2nd Blue Marble)
Putting it all together:
(8/16) x (7/15) = 56/240 = 7/30
Therefore, the probability of drawing two blue marbles, to the nearest 1000th, is approximately 0.2333.
The Unveiling:
We have successfully decoded the mystery of the blue marbles! With a probability of 0.2333, our mathematical journey has led us to a fascinating conclusion.
Now, go forth and explore the world with newfound confidence, knowing that even the most puzzling questions can be unraveled with the power of mathematics!
Question:
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A bag contains 3 red marbles, 8 blue marbles and 5 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 1000th, that both marbles drawn will be blue?
Answer 2
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