There is a bag filled with 3 blue and 5 red marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced.
Another marble is taken at random.
What is the probability of getting exactly 1 blue?

The probability is 0.536

Step-by-step explanation:

We have 3 blue marbles, and 5 red marbles (a total of 3 + 5  = 8 marbles)

First, we take a marble and it is not replaced.

Then we take another marble.

We want to calculate the probability of getting only one blue marble.

Then we have two cases:

1) First we take a blue marble, and after a red marble

2) First we take a red marble, and after a blue marble.

Let's calculate the probability of these two events:

1) The probability of taking a blue marble at random, is equal to the quotient between the number of blue marbles, and the total number of marbles.

this is: p1 = 3/8.

Now we need to take a red marble. Same procedure as before, but now we already taken a marble from the bag, so the total number of marbles is 7 now, and the number of red marbles is 5. The probability here is:

p2 = 5/7

The joint probability (the probability of both events happening) is equal to the product between the individual probabilities, this is:

P = p1*p2 = (3/8)*(5/7) = 0.268

2) Now we first take a red marble, we can calculate the probabilities in the same way than above.

The probability of taking a red marble at first is:

q1 = 5/8

The probability of taking a blue marble in the second draw is:

q2 = 3/7

The joint probability is:

Q = p1*p2 = (5/8)*(3/7) = 0.268

The total probability of getting only one blue marble will be equal to the addition of both the probabilities we found.

Probability = P + Q = 0.268 + 0.268 = 0.536

step-by-step explanation:

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