This is what I have tried so far for 1.a.:

from __future__ import print_function, division import numpy as np import matplotlib.pyplot as plt

def coins(n,p): return np.random.choice([True, False], p=[p,1-p], size=n)

#1.a

array1 = []

count2 = 0

for i in range(0, 10): seq1a = coins(3,0.5) print(seq1a) for j in range(0,len(seq1a)): count1 = 0 if seq1a[j] == seq1a[j-1]: # trying to count for each element being the same count1 +=1 else: count1 += 0 if count1 == 2: #trying to count for each time a trial has identical flips array1.append(True) else: array1.append(False)

for k in range(0, len(array1)): if array1[k] == True: count2 +=1 else: count2 = count2

print(count2/10000) #probability

4 [Coding (10 Points)] Use 10,000 trials to estimate the probabilities in all parts of Problem 1 and parts (a) through (d) in Problem 3. To use simulations for estimating the probability of an event, E, we can run n 10,000 trials and count the number of trials in which the event of interest, E, occurs. Let us call this number ne. Then, the ratio will be an estimate for P(E) 4 [Coding (10 Points)] Use 10,000 trials to estimate the probabilities in all parts of Problem 1 and parts (a) through (d) in Problem 3. To use simulations for estimating the probability of an event, E, we can run n 10,000 trials and count the number of trials in which the event of interest, E, occurs. Let us call this number ne. Then, the ratio will be an estimate for P(E)