Sample Space (10 problems)

What are the three self-evident truths about probabilities?

The following table shows the frequencies for red-green color blindness, where M represents “Person is male” and C represents “Person is color blind”

Find.

A soft drink bottling company maintains records concerning the number of unacceptable bottles of soft drink obtained from the filling and capping machines. Based on past data, the probability that a bottle came from machine I and was nonconforming is 0.05 and the probability that a bottle came from machine II and was nonconforming is 0.025. These probabilities are representing the probability of one bottle out of the total sample having the specified characteristics. Half the bottles are filled on machine I and the other half are filled on machine II.

a. Give an example of a simple event.

b. Give an example of a joint event.

c. If a filled bottle of soft drink is selected at random, what is the probability that it is a nonconforming bottle?

d. If a filled bottle of soft drink is selected at random, what is the probability that it was filled on machine II?

e. If a filled bottle of soft drink is selected at random, what is the probability that it was filled on machine I and is a conforming bottle?

The numbers 1, 2, 3, 4 and 5 are written on slips of paper, and two slips and two slips are drawn at random one at a time without replacement. Find the probability that both numbers are even.

A record is kept each day for three days about whether a particular stock is up or down. Let u = up and d = down. Find S.

Ford Motor Company advertises its cars on radio and on television. The company is interested in assessing the probability that a randomly chosen person is exposed to at least one of these two modes of advertising. If we define event R as the event that a randomly chosen person was exposed to a radio advertisement and event T as the event that the person was exposed to a television commercial, define R U T and R ∩ T in this context.

Consider the event that a player scores a point in a game against team A and the event that the same player scores a point in a game against team B. What is the union of the two events? What is the intersection of the two events?

For a person selected randomly from a certain population, events A and B are defined as follows:

A = event the person is a male.

B = event the person is a smoker.

P(A) = 0.47

P(B) = 0.23

P(A and B) = 0.12.

Find P(A or B).

You roll two fair dice, a blue one and a yellow one

a) write a sample space.

b) Find P (even number on the blue dice and 3 on the yellow dice)

c) Find P ( 3 on the blue dice and even number on the yellow dice)

d) Find P(3 on the blue dice and 4 on the yellow dice)

If you roll a single fair die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?

b.) Assign probabilities to the outcomes of the sample space of part (a). Do the probabilities add up to 1? Should they add up to 1? Explain.

c.) What is the probability of getting a number less than 5 on a single throw?

d.) What is the probability of getting 5 or 6 on a single throw?