Sec. 3.5: Contingency Tables

• A contingency table is a way of organizing data to make finding conditional probabilities easier.

Example 1: Speeding violations and cell phone users

Speeding violation in last year

No speeding violation in last year

Total

Cell phone user

25 280 305

Not a cell phone user

45 405 450

Total 70 685 755

Find the following probabilities:• P(person uses a cell phone)• P(person had no violations

last year)• P(person had no violations

last year and uses a cell phone)

• P(person had a violation given they use a cell phone)

• P(person had no violation given they do not use a cell phone)

Example 2: The following table shows a random sampling of 100 hikers and their preferred hiking area

Sex Coast Lakes Mountains

Total

Female 18 16 45

Male 14 55

Total 41

• Complete the table• Are the events being

female (F) and preferring coastline (C) independent events?

• Find P(F and C)• Find P(F)·P(C)• If M=being male and

L=preferring lakes. Find P

Practice #1: A medical trial into the effectiveness of a new medication was carried out. 120 females and 90 males took part

in the trial. Out of those people, 50 females and 30 males responded positively to the medication. Given below is a

contingency table with the given information filled in.

Female Male Totals

Positive 50 30

Negative

Totals 120 90

• What is the probability that the medicine gives a positive result for females? (P)

• What is the probability that the medicine gives a negative result for males? (P)

• Was the medication's success independent of gender? Explain.

Practice #2: Use the given contingency table to answer the following questions

Brown Eyes

Not Brown Eyes

Totals

Black Hair 50 30

Red Hair 70 80

Totals

• What is the probability that someone with black hair has brown eyes?

• What is the probability that someone has black hair?

• What is the probability that someone has brown eyes?

• Are having black hair and having brown eyes dependent or independent events?