a. To calculate the probability that the marbles picked, without replacement, are in the order purple, red, and blue, we need to consider the number of each color of marbles and the total number of marbles.
Total number of marbles = 5 (red) + 7 (blue) + 9 (purple) = 21 marbles
The probability of picking a purple marble first is 9/21.
After picking a purple marble, there are 8 purple marbles left out of 20 remaining marbles.
The probability of picking a red marble next is 5/20.
Finally, after picking a purple and a red marble, there are 4 red marbles left out of 19 remaining marbles.
The probability of picking a blue marble last is 4/19.
To find the combined probability, we multiply the individual probabilities:
Probability = (9/21) * (5/20) * (4/19) = 0.033 or 3.3%
Therefore, the probability that the marbles picked, without replacement, are in the order purple, red, and blue is approximately 3.3%.
b. To calculate the probability that the marbles picked, with replacement, are all purple in color, we can consider the probability of picking a purple marble on each draw, assuming each draw is independent.
The probability of picking a purple marble on each draw is 9/21.
Since we are replacing the marbles after each draw, the probabilities remain the same for each draw.
To find the combined probability, we multiply the individual probabilities:
Probability = (9/21) * (9/21) * (9/21) = (9/21)^3 = 0.107 or 10.7%
Therefore, the probability that the marbles picked, with replacement, are all purple in color is approximately 10.7%.