Exam 4: Probability: the Study of Randomness

Suppose you have two math classes (math 1 and math 2)and two sciences courses (science 1 and science 2)that you must complete before your sophomore year in college.Assume your college is on a semester system and there are two semesters in each year.Suppose you are required to take exactly one of the science courses and exactly one of the math courses during your sophomore year.What is the event A of required math and science courses you could take the first semester of your sophomore year?

A study was conducted in a large population of adults concerning eyeglasses for correcting reading vision.Based on an examination by a qualified professional,the individuals were judged as to whether or not they needed to wear glasses for reading.In addition it was determined whether or not they were currently using glasses for reading.The following table provides the proportions found in the study. If a single adult is selected at random from this large population,what is the probability that the adult is judged to need eyeglasses for reading?

If you draw an M&M candy at random from a bag of the candies,the candy you draw will have one of six colors.The probability of drawing each color depends on the proportion of each color among all candies made.Assume the table below gives the probabilities for the color of a randomly chosen M&M. What is the probability that you draw neither a brown nor a green candy?

There are five upper-level mathematics courses that are required for math majors at a certain university.You can only pass the last course after you have passed all of the other four.Passing the last course is considered a(n)________ event.

You decide to visit the health center to be tested for HIV,the virus that causes AIDS.What is the sample space that represents your possible result?

The Dallas Cowboys are a team that is part of the National Football League.What is the sample space for the outcome of their next game against the Green Bay Packers?

The number of hours of sleep you had last night is an example of a ______ random variable.

The probability of an event is defined as the proportion of times an event occurs occasionally.

Probability distributions can be visualized graphically using a _______ for discrete random variables.

Suppose you have two math classes (math 1 and math 2)and two sciences courses (science 1 and science 2)that you must complete before your sophomore year in college.Assume your college is on a semester system and there are two semesters in each year.Suppose you are required to take at least one of the science courses during your freshman year.What is the event A of required science courses you could take the first semester of your freshman year?

The second letter of a word in a text message is independent of the first letter of that word.

What is the probability Z = 0? (The figure below is a standard Normal probability distribution. )

Suppose you have two math classes (math 1 and math 2)and two sciences courses (science 1 and science 2)that you must complete before your sophomore year in college.Assume your college is on a semester system and there are two semesters in each year.Suppose you are only allowed to take one of the required courses during the first semester of your freshman year.What is the sample space for the course you take?

Suppose you have a perfectly fair 10-sided die,with sample space S = {1,2,3,4,5,6,7,8,9,10}.Now suppose that the 10-sided die is rolled twice in a row.What is the probability of rolling a 9 on the second roll if a 9 was rolled on the first roll?

The statistics of a particular basketball player state that he makes 4 out of 5 free-throw attempts.During a season,the basketball player makes an average of about 200 free-throw attempts.On how many of these throws would you estimate he will actually score a point?

A phenomenon is observed many,many times under identical conditions.The proportion of times a particular event A occurs is recorded.What does this proportion represent?

For an event to be random (e.g. ,flipping a coin five times),a cluster of the same observations (e.g. ,all heads)would not be possible.

Suppose a fair coin is flipped twice and the number of heads is counted.Which of the following is a valid probability model for the number of heads observed in two flips?

Suppose that A and B are two independent events.The probability that event A occurs is P(A)= 0.4 and that B occurs is P(B)= 0.2.What is the probability that A does not occur and that B also does not occur?

Which of the following are independent trials?