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HW #19 - Probability

1. (IN CLASS) A survey of college students finds that 40% like country music, 30% like gospel music, and 10% like both.

A) What percent of college students like country but not gospel?

B) What percent like neither gospel nor country?

2. (ANSWER GIVEN) A study of students in a college class finds that 70% are from a local high school and 75% are under 25 years old and that 65% are both local and under 25.

A) What percent are 25 or over?

B) What percent are 25 or over and not from a local high school?

3. (SOLUTION GIVEN) In a surgery for a torn tendon there is 3% chance of infection and a 14% chance the torn tendon will not repair properly and a 1% chance of both. What percent of these operations are successful and are free from infection?

4. (HOMEWORK) Suppose in a group of people getting ready to vote that 63% favor Amendment A and 48% favor Amendment B and 41% favor both amendments.

A) What percent of people in this group favor neither amendment?

B) What percent favor Amendment B, but not A?

5. (ALTERNATE HW) In a certain city 34% of homes have a dog, 42% have a cat, and 16% have both. You choose a house at random.

A) What is the probability the house has a cat but not a dog?

B) What is the probability the house has neither a car nor a dog?

6. (IN CLASS) Suppose you are a car salesman and when a customer comes in you have a 15% chance of making a sale. If 9 customers come in on a certain day what is the probability you will make at least one sale?

7. (ANSWER GIVEN) Suppose you have a string of 25 Christmas lights in which if anyone light fails the whole string will not light. Suppose the probability that any one light will fail is 4%. What is the probability that when plugged in, the string of lights will disappoint you?

8. (SOLUTION GIVEN) Suppose a professor has a class with 200 students. What is the probability that at least one student will have their birthday on Valentine’s Day? (Assume 365 days in a year)

9. (HOMEWORK) People with O- blood are universal donors. That is, any patient can receive a transfusion of O- blood. Only 7.2% of Americans have O- blood. If 8 people appear at random, what is the probability that at least one of them is a universal donor?

10. (ALTERNATE HW) Suppose in a population that 2% of a population is infected with the HIV virus. Suppose a blood product is made by combining blood from 50 donors. What is the probability that this blood product will contain the blood from someone with HIV?

11. (IN CLASS) A survey of college students finds that 40% like country music, 30% like gospel music, and 10% like both.

C) If a student likes gospel, what is the probability they like country?

D) If a student likes country, what is the probability they like gospel?

12 (ANSWER GIVEN) A study of students in a college class finds that 70% are from a local high school and 75% are under 25 years old and that 65% are both local and under 25.

C) If a student is younger than 25, what is the probability they are from a local high school?

D) If a student is from a local high school, what is the probability they are younger than 25?

13 (SOLUTION GIVEN) In a surgery for a torn tendon there is 3% chance of infection and a 14% chance the torn tendon will not repair properly and a 1% chance of both.

B) If the surgery is successful, what is the probability there is no infection?

C) If there is no infection, what is the probability the surgery will be successful?

14. (HOMEWORK) Suppose in a group of people getting ready to vote that 63% favor Amendment A and 48% favor Amendment B and 41% favor both amendments.

C) If a person favors Amendment A, what is the probability they favor Amendment B?

D) If a person favors Amendment B, what is the probability they favor Amendment A?

15. (ALTERNATE HW) In a certain city 34% of homes have a dog, 42% have a cat, and 16% have both. You choose a house at random.

C) If a home has a cat, what is the probability it has a dog also?

D) If a home has a dog, what is the probability it has a cat also?

16. Here are the number of full-time faculty in graduate departments of Sociology by rank and gender for 2000-2001.

| |Instructor |Assistant Professor |Associate Professor |Full Professor |Total |

|Female |61 |565 |502 |476 |1604 |

|Male |39 |618 |683 |1383 |2723 |

|Total |100 |1183 |1185 |1859 |4327 |

A) (IN CLASS) What percent are full professors?

B) (ANSWER GIVEN) What percent are female?

C) (SOLUTION GIVEN) What percent are assistant professors?

D) (HOMEWORK) What percent are associate professors?

E) (ALTERNATE HW) What percent are male?

You pick one full-time faculty at random.

F) (IN CLASS) What is the probability the person is male given they are a full professor?

G) (ANSWER GIVEN) What is the probability the person is male given they are an assistant professor?

H) (SOLUTION GIVEN) What is the probability the person is a female given they are an assistant professor?

I) (HOMEWORK) What is the probability the person is a female given they are an associate professor?

J) (ALTERNATE HW) What is the probability the person is a male given they are an associate professor?

K) (IN CLASS) What is the probability the person is a full professor given they are male?

L) (ANSWER GIVEN) What is the probability the person is an assistant professor given they are male?

M) (SOLUTION GIVEN) What is the probability the person is an assistant professor given they are female?

N)(HOMEWORK) What is the probability the person is an associate professor given they are female?

O) (ALTERNATE HW) What is the probability the person is an associate professor given they are male?

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