What are the chances?

Introduction to Statistics in Python

Maggie Matsui

Content Developer, DataCamp

Measuring chance

What's the probability of an event?

$$ P(\text{event}) = \frac{\text{\# ways event can happen}}{\text{total \# of possible outcomes}} $$

Example: a coin flip

$$ P(\text{heads}) = \frac{\text{1 way to get heads}}{\text{2 possible outcomes}} = \frac{1}{2} = 50\%$$

Number line of probability. 0 percent = impossible, 100 percent = will certainly happen

Box with Amir, Brian, Claire, and Damian's names

Pulling out Brian's name

$$P(\text{Brian}) = \frac{1}{4} = 25\%$$

print(sales_counts)

     name  n_sales
0    Amir      178
1   Brian      128
2  Claire       75
3  Damian       69

sales_counts.sample()

    name  n_sales
1  Brian      128

sales_counts.sample()

     name  n_sales
2  Claire       75

np.random.seed(10)

sales_counts.sample()

    name  n_sales
1  Brian      128

np.random.seed(10)
sales_counts.sample()

    name  n_sales
1  Brian      128

np.random.seed(10)
sales_counts.sample()

    name  n_sales
1  Brian      128

Sampling without replacement

Box with Amir, Claire, Damian

Claire's name pulled out

$$P(\text{Claire}) = \frac{1}{3} = 33\%$$

sales_counts.sample(2)

     name  n_sales
1   Brian      128
2  Claire       75

GIF of hand reaching into box, pulling out Brian's name, then dropping it back in

Screen Shot 2020-04-28 at 5.21.54 PM.png

$$P(\text{Claire}) = \frac{1}{4} = 25\%$$

sales_counts.sample(5, replace = True)

     name  n_sales
1   Brian      128
2  Claire       75
1   Brian      128
3  Damian       69
0    Amir      178

Two events are independent if the probability of the second event isn't affected by the outcome of the first event.

Two columns: First pick column containing Amir, Brian, Claire, Damian. Second pick column is empty

Two events are independent if the probability of the second event isn't affected by the outcome of the first event.

Sampling with replacement = each pick is independent

Arrows from each name in first pick column point to Claire in second pick column, with probability 25%

Two events are dependent if the probability of the second event is affected by the outcome of the first event.

Two columns: First pick column containing Amir, Brian, Claire, Damian. Second pick column is empty

Two events are dependent if the probability of the second event is affected by the outcome of the first event.

Claire in first column points to Claire in second column with probability 0%

Two events are dependent if the probability of the second event is affected by the outcome of the first event.

Sampling without replacement → picks become dependent

Amir, Brian, and Damian in first column points to Claire in second column with probability 33%

Introduction to Statistics in Python