dis06_solutions

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Data 8 Fall 2023 Iteration, Conditionals Week 06 September 2023 Welcome to the Week 6 Discussion Worksheet! This week we will be discussing conditional statements and iteration, which are powerful computational tools that we will use throughout the course. Conditional statements allow data scientists to make more complex decisions with their code, while for loops allow us to repeat the same action many times. 1. Funky Function What does the mystery function do? Write a sentence below describing what the function’s inputs should be and what the function does. Hint: Try out the function on a few different inputs and see what happens! def mystery(n1, n2): if n2 - n1 > 0: return n2 - n1 elif n2 - n1 < 0: return n1 - n2 else: return 0 The function takes in two different numbers and computes the absolute difference between them. 1

2. Getting Even a. The % operator returns the remainder if you divide by a certain number (e.g. 11%5 = 1 ). If a number n is odd, what will n %2 return? 1. If a number is even, n %2 will return 0. b. The count evens function takes in an array of integers and returns the number of even integers in the array. Use a combination of iteration and conditionals to complete the skeleton code below. def count evens(n array): num evens = 0 for : if : return def count evens(n array): num evens = 0 for num in n array: if num % 2 == 0: num evens = num evens + 1 return num evens c. Now let’s see how we can write the same function using array operations instead of iteration. def count evens(n array): remainder array = return def count evens(n array): remainder array = n array % 2 return np.count nonzero(remainder array == 0) Alternate Solution: def count evens(n array): remainder array = n array % 2 return len(remainder array) - sum(remainder array) 2

3. Marble Madness Ron has a bag with three marbles. Two of them are purple, and one is orange. Each round he draws from the bag 10 times with replacement. He wins the round by drawing at least one orange marble. a. Write a function to simulate one round of Ron’s game. The function should return True if he wins and False if he loses. def one round(): balls = one sim = num orange = return def one round(): balls = make array(‘purple’, ‘purple’, ‘orange’) one sim = np.random.choice(balls, 10) num orange = sum(one sim == ‘orange’) return num orange >= 1 Instead of sum, students can also use np.count nonzero() . They can also use sample proportions with probabilities (2/3, 1/3). b. Finish the following code to help Ron simulate 100 rounds of the game and assign the variable win proportion to the proportion of rounds he wins. count = 0 for : if : win proportion = count = 0 for i in np.arange(100): if one round(): count = count + 1 win proportion = count / 100 c. For any one draw, what is the probability that Ron draws a purple marble? 3

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P(Drawing a purple marble) = 2 3 d. For any individual round, what is the probability that Ron loses? Using the multiplication rule: P(Ron loses one round) = P(drawing 10 purple balls) = P(purple) 10 = ( 2 3 ) 10 e. For any individual round, what is the probability that Ron wins? Using the complement rule: P(Ron wins one round) = 1 - P(Ron loses) = 1 - ( 2 3 ) 10 4

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