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# Tree Diagram probabilities

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There is a bag filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?

Jun 6, 2023

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The probability of getting exactly 1 blue marble is 2/7.

The probability of getting a blue marble on the first draw is 3/7.

The probability of getting a red marble on the second draw is 4/7.

The probability of getting exactly 1 blue marble is the product of these two probabilities, which is 2/7.

Another way to solve this problem is to use the fact that the probability of getting a certain outcome is equal to the number of ways to get that outcome divided by the total number of possible outcomes.

The total number of possible outcomes is 7, because there are 7 marbles in the bag.

There are 2 ways to get exactly 1 blue marble, because you can either get a blue marble on the first draw and a red marble on the second draw, or you can get a red marble on the first draw and a blue marble on the second draw.

Therefore, the probability of getting exactly 1 blue marble is 2/7.

Jun 6, 2023