A bag contains 5 red and 3 blue marbles. Two marbles are drawn at random without replacement. What is the probability that they are of different colors?
Correct: B
Total number of marbles in the bag = 5 red + 3 blue = 8 marbles.
We are drawing two marbles at random without replacement.
First, let's find the total number of ways to choose 2 marbles from 8.
This is given by the combination formula C(n, k) = n! / (k! * (n-k)!).
Total ways to choose 2 marbles from 8 = C(8,2) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28.
Next, we need to find the number of ways to draw two marbles of different colors. This means one red marble AND one blue marble.
Number of ways to choose 1 red marble from 5 = C(5,1) = 5.
Number of ways to choose 1 blue marble from 3 = C(3,1) = 3.
Number of ways to choose one red and one blue marble = C(5,1) * C(3,1) = 5 * 3 = 15.
Finally, the probability is the ratio of favorable outcomes to the total possible outcomes:
Probability = (Number of ways to choose different colors) / (Total number of ways to choose 2 marbles)
Probability = 15 / 28.