A box contains three red marbles and six blue marbles. What is the probability of selecting at random, without replacement, two blue marbles? show all steps
Step 1: Calculate the total number of marbles in the box
Total number of marbles = 3 (red) + 6 (blue) = 9 marbles
Step 2: Calculate the probability of selecting the first blue marble
Probability of selecting a blue marble = Number of blue marbles / Total number of marbles
Probability of selecting a blue marble = 6 / 9 = 2/3
Step 3: Calculate the probability of selecting the second blue marble without replacement
After selecting the first blue marble, there are now 5 blue marbles left and a total of 8 marbles remaining in the box (since one blue marble has already been selected).
Probability of selecting a second blue marble = Number of remaining blue marbles / Total number of remaining marbles
Probability of selecting a second blue marble = 5 / 8
Step 4: Multiply the probabilities of selecting the two blue marbles
Probability of selecting two blue marbles = Probability of selecting the first blue marble * Probability of selecting the second blue marble
Probability of selecting two blue marbles = (2/3) * (5/8) = 10/24 = 5/12
Therefore, the probability of selecting at random, without replacement, two blue marbles from the box is 5/12 or approximately 0.417 (41.7%).