MATH 215- Probability and Statistics: Introduction to Statistics Assignment 2

Overview

This assignment covers content from Unit 2 of the course. It assesses your knowledge of the concepts and rules that allow us to compute the probabilities related to events that occur when conditions are uncertain.
Instructions
•    Show all your work and justify all of your answers and conclusions, except for the True/False questions.
•    Keep your work to 4 decimals, unless otherwise stated.

1. 1. Circle True (T) or False (F) for each of the following statements:
      T    F    {H, T} represents the sample space for an experiment of flipping two coins, each with heads (H) on one side and tails (T) on the other.
      T    F    13/12 represents a possible value of a probability.
      T    F    Suppose that the probability of event A occurring is 1/5 and the probability of event B occurring is 3/7. If events A and B are mutually exclusive, the probability that A and B occur together is 0.
      T    F    If a researcher samples without replacement, then future probabilities of the sampling process are unaffected by prior probabilities.
      
      
   2.  At a recent convention, a group of 60 doctors were classified according to their specialties. The number of doctors in each specialty was summarized as follows:
      Pediatrician: 18 General Practitioner: 29 Surgeon: 4 Dermatologist: 9
      If a doctor is selected at random, what is the probability that

1. 1. the doctor is a dermatologist?
   2. the doctor is either a pediatrician or a general practitioner?
   3. the doctor is not a pediatrician?
   4. the doctor is neither a general practitioner nor a dermatologist?

3.  An analysis of blood donors examined blood type (A, B, AB or O) and whether the donor was male or female. The data is represented in the following table:

   
In the questions below, round all calculated probabilities to 4 decimal places.

1. 1. What is the probability that a randomly selected donor is female?
   2. What is the probability that a randomly selected donor is either male or has type O blood?
   3. What is the probability that a randomly selected donor is neither female nor has type AB blood?
   4. What is the probability that a selected donor has type AB blood, given that he is male?
   5. Are the events that a person has type A blood (denoted by A) and that a person is female (denoted by F) mutually exclusive? Explain.
   6. Are the events that a person has type B blood (denoted by B) and that a person is female (denoted by F) independent? Justify your conclusion using the appropriate rule(s) of probability.

4.  Three patients are accepted into a clinical trial for a new drug. According to the severity of the condition of each patient, the doctors estimate that the probability that the drug will be effective for Patient A is 0.7, the probability that it will be effective for Patient B is 0.2, and the probability that it will be effective for Patient C is 0.6. Assume that the success of the drug for the three patients is independent.

a.    Draw a tree diagram displaying all outcomes and joint probabilities measuring the effectiveness of the drug for all three patients.
b.    What is the probability that the drug will be effective for Patient B only?
c.    What is the probability that the drug will be effective for at least one of the patients?
d.    What is the probability that the drug will be effective for exactly two of the three patients?

5.    The Math Club is picking names out of a hat to determine who will serve as the Executive for their group. The person whose name is drawn first will serve as the President, and the person whose name is drawn second will be Vice-President. The Math Club has 13 members: 5 members whose focus of study is Statistics and 8 members whose focus of study is Calculus. [Hint: A tree diagram would be helpful in analyzing this problem.]

What is the probability that:

a.    Both members chosen for the executive have Calculus as their focus of study?
b.    Any one member of the Executive has Statistics as a focus, and the other has Calculus as a focus?
c.    The chosen President has Calculus as a focus and the chosen Vice-President has Statistics as a focus?
d.    At least one member of the chosen Executive has a focus in Calculus?

6.    A survey questioned 200 individuals regarding their intention to vote (Conservative, Liberal or Other) in an upcoming election. It was found that 50% of the sample planned to vote Conservative and 40% planned to vote Liberal. Fifty percent of the men indicated that they planned to vote Liberal, and forty percent of the men planned to vote Conservative. Overall, 30% of the sample were women.

a.    Construct a two-way classification for these survey results.
b.    Circle True (T) or False (F) for the following statement:
T F    In this example, male and female are complementary events.

7.    You are given the probabilities of events A, B and C as listed below:
   

a.    Find  .
b.    Find  .
c.    Find  .
d.    Are B and C mutually exclusive events? Why?
e.    Are B and C independent events? Provide a mathematical justification of your conclusion using the appropriate rule(s) of probability.

These extra pages are for additional calculations. If you need them for your solutions, please reference them in the appropriate place in the questions.