Contingency Tables – Continued

October 10, 2023

Contingency Tables are one way to organise data. Here is a data summary of computer users in a group.

	PC	Mac	Row Totals
Male	45	38	83
Female	40	55	95
Column Totals	85	93	178

Joint Probability

What is the joint probability of Female and Mac?
First, the answer: go to the cell at the junction of Female and Mac, i.e., 55 and divide by the total. 55/178 = 0.309.

Now the theory:
P (F AND Mac) = P(F | Mac) x P(Mac)
P(F | Mac) = 55/93
P(Mac) = 93/178
P (F AND Mac) = (55/93) x (93/178) = 55/178 = 0.309.

	PC	Mac	Row Totals
Male	45/178 = 0.25	38/178 = 0.21
Female	40/178 = 0.22	55/178 = 0.31
Column Totals

Conditional Probabilities

Conditional probability is the probability that an event occurs, given another event has happened. Given that a customer is female, what is the probability she’ll purchase a Mac?

The answer is female-Mac cell (55) and divide it with the female row total (95). 55/95 = 0.58.

	PC	Mac	Row Totals
Male	P(P\|M) 45/83	P(M\|M) 38/83	83
Female	P(P\|F) 40/95	P(M\|F) 55/95	95
Column Totals	85	93	178

	PC	Mac	Row Totals
Male	P(M\|P) 45/85	P(M\|M) 38/93	83
Female	P(F\|P) 40/85	P(F\|M) 55/93	95
Column Totals	85	93	178