Q2.1: You have a bag of 12 marbles, 6 are red, 4 are white, and 2 are blue. You randomly pick three marbles from the bag. What is the probability of drawing 1 red, 1 white, and 1 blue (in this order)? The theoretical result is 2/55 -3.636%. Write a simulation of 100,000 trials to verify the answer Hint. You can follow the steps here: 1. Create an array of 12 elements, bag = np.array(lr,r, rrrrww.w w,b', b']) 2. Create the desired outcome of 3 marbels of red, white, and blue, bag3 = np array(l'r' w b'l) 3. For each of the trial, you use np.random permutation() to shuffle the bag array 4. Create a Boolean array by comparing the first three elements of the shuffled array with the desired outcome 5. If the values the Boolean array are all True -> you have a match

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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help using numpy both parts please

Q2.1: You have a bag of 12 marbles, 6 are red, 4 are white, and 2 are blue. You randomly pick
three marbles from the bag. What is the probability of drawing 1 red, 1 white, and 1 blue (in this
order)? The theoretical result is 2/55 -3.636%. Write a simulation of 100,000 trials to verify the
answer.
Hint. You can follow the steps here:
1. Create an array of 12 elements, bag = np array(l'r,r,rrrrwwww. b'b'])
2. Create the desired outcome of 3 marbels of red, white, and blue, bag3 = np.array(l'r w. 'b'])
3. For each of the trial, you use np.random.permutation() to shuffle the bag array
4. Create a Boolean array by comparing the first three elements of the shuffled array with the
desired outcome.
5. If the values the Boolean array are all True - you have a match
In [ ]:
Q2.2 With the same bag, you again pick out three marbles. However, the order does not matter
this time. What is the probability of drawing 1 red, 1 white, and 1 blue? The theoretical result is
12/55 -21.82%. Write a simulation of 100,000 trials to verify the answer
Hint. This question is different from Q2.1 since the order of the drawing is not important as long as
you have (rw,b) in the outcome. You should look for another way to compare the desired outcome
with the shuffled arrays.
Transcribed Image Text:Q2.1: You have a bag of 12 marbles, 6 are red, 4 are white, and 2 are blue. You randomly pick three marbles from the bag. What is the probability of drawing 1 red, 1 white, and 1 blue (in this order)? The theoretical result is 2/55 -3.636%. Write a simulation of 100,000 trials to verify the answer. Hint. You can follow the steps here: 1. Create an array of 12 elements, bag = np array(l'r,r,rrrrwwww. b'b']) 2. Create the desired outcome of 3 marbels of red, white, and blue, bag3 = np.array(l'r w. 'b']) 3. For each of the trial, you use np.random.permutation() to shuffle the bag array 4. Create a Boolean array by comparing the first three elements of the shuffled array with the desired outcome. 5. If the values the Boolean array are all True - you have a match In [ ]: Q2.2 With the same bag, you again pick out three marbles. However, the order does not matter this time. What is the probability of drawing 1 red, 1 white, and 1 blue? The theoretical result is 12/55 -21.82%. Write a simulation of 100,000 trials to verify the answer Hint. This question is different from Q2.1 since the order of the drawing is not important as long as you have (rw,b) in the outcome. You should look for another way to compare the desired outcome with the shuffled arrays.
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