Probability Problem
- With 5. Draw a picture. We can associate the 2 numbers with a point on the x-y axis.
0<=x<=1,0<=y<=1 - With 6. Ask a simpler version of the problem
What is the region on the graph that x/y will round down to 0?
- Answer: y needs to be bigger than x, so it is the area above the y=x
What is the region on the graph that x/y will round down to 2?
- Answer: x needs to be equal or greater than y twice && x needs to be smaller than y 3 times. Thus it is the area below y=x/2, above y=x/3x
Answer is basically sum of the triangles on the graph
Take advantage of Python codes to obtain an answer
!pip3 install numpy import numpy as np data_size = 10**6 x = np.random.random(data_size) y = np.random.random(data_size) ratios = x / y round_down_ratio = np.floor(ratios) even_ratio_res = (round_down_ratio % 2 == 0).mean()