MSM 709

Additional probability examples (Ch. 5)

 

Ex. 1

In a group of 325 first year students, 250 are listed as taking a math course and 197 are listed as taking a biology course.  Of those, 150 students are taking both a math and a biology course.

 

A student is selected at random from this group.  What is the probability the student selected is taking

1.                  a course in at least one of these two subjects?

2.                  neither subject?

3.                  a math course but not a biology course?

4.                  a biology course, given that the student is taking a math course?

 

Ex. 2

A card is selected from an ordinary deck of 52.  Define the following events:

            R: the card is red

            H: the card is a heart

            S: the card is a spade

1.                  Find P(H), P(H|R), P(S|R), P(S|Rc).

2.                  Are the events R and H independent?  Are they disjoint?

3.                  Are the events R and S independent?  Are they disjoint?

4.                  Are the events H and S independent?  Are they disjoint?

 

Ex. 3

Ninety-five percent of a group of adults is either male or has graduated from high school.  The group is 60% male, and 80% of the group have graduated from high school.

1.                  Of the high school graduates, what proportion is male?

2.                  Of the males, what proportion are high school graduates?

3.                  What is the probability that a female in the group is a high school graduate?

 

Ex. 4

Twenty-seven percent of the inmates in state prisons are first-time offenders.  Of the first-time offenders, 72% are convicted of violent crimes.

 

If a prisoner is selected at random from the state prison system, what is the probability he is a first-time offender convicted of a violent crime?

 

 

Ex. 6

A test for a certain disease is found to be 95% accurate; that is, if the person has the disease, the probability the test reads “positive” is 0.95.  Also, if the person does not have the disease, the probability that the test reads “negative” is also 0.95.  It is known that approximately 2% of the population is afflicted with the disease.  A person from this population does not know his disease status and gets tested for the disease.  What is the probability that this test gives a false positive result?