Conditional probability

Introduction to Statistics

George Boorman

Curriculum Manager, DataCamp

Multiple meetings

Sampling without replacement

Box with Amir, Claire, Damian.png

Sampling without replacement

Claire's name pulled out.png

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

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.png

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%.png

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%.png

Conditional probability is used to calculate the probability of dependent events
- The probability of one event is conditional on the outcome of another

¹ Image credit: https://unsplash.com/@pixeldan

venn_diagram_showing_two_events_and_an_overlap_where_both_events_occur.png

venn_diagram_number_of_orders_over_150_dollars_and_number_kitchen_orders.png

venn_diagram_number_of_orders_over_150_dollars_and_number_kitchen_orders.png

$$P(Order > 150 | Kitchen) = \frac{\frac{20}{1767}}{\frac{181}{1767}}$$

$$P(Order > 150 | Kitchen) = \frac{20}{181} $$

venn_diagram_number_of_kitchen_orders_and_orders_over_150_dollars.png

$$P(Kitchen | Order > 150) = \frac{\frac{20}{1767}}{\frac{601}{1767}}$$

$$P(Kitchen | Order > 150) = \frac{20}{601} $$

$$P(A | B) = \frac{{P(A \ \cap \ B)}}{{P(B)}}$$

$P(A | B)$ → Probability of event A, given event B
$P(A \ \cap \ B)$ → Probability of event A and event B
- Divided by the probability of event B → $P(B)$

Introduction to Statistics