What are the chances?

Introduction to Statistics in R

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

Assigning salespeople

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

Assigning salespeople

Pulling out Brian's name

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

Sampling from a data frame

sales_counts

   name  n_sales
 1 Amir      178
 2 Brian     126
 3 Claire     75
 4 Damian     69

sales_counts %>%
  sample_n(1)

   name  n_sales
 1 Brian     126

sales_counts %>%
  sample_n(1)

   name  n_sales
 1 Claire     75

Setting a random seed

set.seed(5)

sales_counts %>%
  sample_n(1)

   name  n_sales
 1 Brian     126

set.seed(5)

sales_counts %>%
  sample_n(1)

   name  n_sales
 1 Brian     126

A second meeting

Sampling without replacement

Box with Amir, Claire, Damian

A second meeting

Claire's name pulled out

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

Sampling twice in R

sales_counts %>%
  sample_n(2)

   name  n_sales
 1 Brian     126
 2 Claire     75

Sampling with replacement

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

Sampling with replacement

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

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

Sampling with replacement in R

sales_counts %>%
  sample_n(2, replace = TRUE)

   name  n_sales
 1 Brian     126
 2 Claire     75

5 meetings:

sample(sales_team, 5, replace = TRUE)

   name  n_sales
 1 Brian     126
 2 Claire     75
 3 Brian     126
 4 Brian     126
 5 Amir      178

Independent events

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

Independent events

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%

Dependent events

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

Dependent events

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%

Dependent events

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

Sampling without replacement = each pick is dependent

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

Let's practice!

Introduction to Statistics in R