A bag contains 4 green marbles, 6 red marbles, and 2 white marbles. Three marbles are drawn at random with replacement. With replacement means that after a marble is drawn, it is replaced before the next one is drawn. Find the probability of all three blue.
Due to the replacement, the three drawings are independent.
However the answer is zero because there are no blue marbles in the bag.
To find the probability of drawing all three blue marbles, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
Since we are drawing three marbles with replacement, each draw has 12 possible outcomes (4 green + 6 red + 2 white = 12), and as we replace each drawn marble, the number of total outcomes remains the same for each draw. Hence, the total number of outcomes is 12 * 12 * 12 = 1728.
Favorable outcomes:
To get all three blue marbles, we need to have blue marbles in all three draws. However, given that there are no blue marbles in the bag, the number of favorable outcomes is zero.
Therefore, the probability of drawing all three blue marbles is 0/1728 = 0.