3.4 Contingency Tables

Suppose a study of speeding violations and drivers who use cell phones produced the following fictional data:

The total number of people in the sample is 755. The row totals are 305 and 450. The column totals are 70 and 685. Notice that 305 + 450 = 755 and 70 + 685 = 755.

Calculate the following probabilities using the table.

a. Find P(Driver is a cell phone user).
b. Find P(driver had no violatio…

a. Complete the table.

b. Are the events "being a woman" and "preferring the coastline" independent events?

Let F = being a woman and let C = preferring the coastline.

1. Find P(F AND C).
2. Find P(F)P(C)

Are these two numbers the same? If they are, then F and C are independent. If they are not, then F and C are not independent.

c. Find the probability that a person is a man given that the person prefers hiking near lakes and streams. Let M = being a man, and let L = prefers hiking near lakes and streams.

1. What word tells you this is a conditional?
2. Fill in the blanks and calculate the probability: P(___|___) = ___.
3. Is the sample space for this problem all 100 hikers? If not, what is it?

d. Find the probability that a person is a woman or prefers hiking on mountain peaks. Let F = being a woman, and let P = prefers mountain peaks.

1. Find P(F).
2. Find P(P).
3. Find P(F AND P).
4. Find P(F OR P).

Verify the remaining entries.

a. Complete the probability contingency table. Calculate the entries for the totals. Verify that the lower-right corner entry is 1.

b. What is the probability that Alissa does not catch Muddy?

c. What is the probability that Muddy chooses Door One OR Door Two given that Muddy is caught by Alissa?

TOTAL each column and each row. Total data = 4,520.7

1. Find P(Year 2 AND Robbery).
2. Find P(Year 3 AND Burglary).
3. Find P(Year 3 OR Burglary).
4. Find P(Year 4 | Vandalism).
5. Find P(Vehicle | Year 1).

Find P(musician is a man AND had private instruction).

Are the events “being a woman musician” and “learning music in school” mutually exclusive events?

Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispani…

Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispani…

Use the following information to answer the next seven exercises. An article in the New England Journal of Medicine, reported about a study of smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispani…

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

What is the probability that a randomly selected senator has an “Other” affiliation?

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

What is the probability that a randomly selected senator is a Democrat and up for reelection in Year B?

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

Suppose that a member of the U.S. Senate is randomly selected. Given that the randomly selected senator is up for reelection in Year B, what is the probability that this senator i…

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

The events “Republican” and “Up for reelection in Year B” are ________

1. mutually exclusive.
2. independent.
3. both mutually exclusive and independent.
4. neither mutually exclusive nor in…

Use the information in the the table to answer the next eight exercises. The table shows the political party affiliation for various members of the U.S. Senate during two separate years when they are up for reelection.

the table gives the number of participants in the recent National Health Interview Survey who had been treated for cancer in the previous 12 months. The results are sorted by age,…

Find P(hit was made by Ty Cobb|The hit was a Home Run).

1. $\frac{4189}{12351}$
2. $\frac{117}{1723}$
3. $\frac{ 1723}{4189}$
4. $\frac{ 117}{12351}$

In a previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News. The factual data were compiled into the following table.

For the following, suppose that you randomly select one player from the 49ers or Cowboys.

1. Find the probability that his shirt number is from 1 to 33.
2. Find the probability that he weighs at most 210…