Answer: The probability is 0.536
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