Exam 4: Introduction to Probability

Six vitamin and three sugar tablets identical in appearance are in a box. One tablet is taken at random and given to Person A. A tablet is then selected and given to Person B. What is the probability that a. Person A was given a vitamin tablet? b. Person B was given a sugar tablet given that Person A was given a vitamin tablet? c. neither was given vitamin tablets? d. both were given vitamin tablets? e. exactly one person was given a vitamin tablet? f. Person A was given a sugar tablet and Person B was given a vitamin tablet? g. Person A was given a vitamin tablet and Person B was given a sugar tablet?

A survey of a sample of business students resulted in the following information regarding the genders of the individuals and their selected major. Selected Major Gender Management Marketing Others Total Male 40 10 30 80 Female 30 20 7 120 Total 7 30 100 200 a. What is the probability of selecting an individual who is majoring in Marketing? b. What is the probability of selecting an individual who is majoring in Management, given that the person is female? c. Given that a person is male, what is the probability that he is majoring in Management? d. What is the probability of selecting a male individual?

Assuming that each of the 52 cards in an ordinary deck has a probability of 1/52 of being drawn, what is the probability of drawing a black ace?

Assume that in your hand you hold an ordinary six-sided die and a dime. You toss both the die and the dime on a table. a. What is the probability that a head appears on the dime and a six on the die? b. What is the probability that a tail appears on the dime and any number more than 3 on the die? c. What is the probability that a number larger than 2 appears on the die?

An applicant has applied for positions at Company A and Company B. The probability of getting an offer from Company A is 0.4, and the probability of getting an offer from Company B is 0.3. Assuming that the two job offers are independent of each other, what is the probability that a. the applicant gets an offer from both companies? b. the applicant will get at least one offer? c. the applicant will not be given an offer from either company? d. Company A does not offer her a job, but Company B does?

A bank has the following data on the gender and marital status of 200 customers. Male female single 20 30 married 100 50 a. What is the probability of finding a single female customer? b. What is the probability of finding a married male customer? c. If a customer is female, what is the probability that she is single? d. What percentage of customers is male? e. If a customer is male, what is the probability that he is married? f. Are gender and marital status mutually exclusive? g. Is marital status independent of gender? Explain using probabilities.

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 4 customers and determining whether or not they purchase any merchandise. How many sample points exist in the above experiment? Note that each customer is either a purchaser or non-purchaser.)

If A and B are independent events with PA) = 0.2 and PB) = 0.6, then PA ∪ B) =

The set of all possible sample points experimental outcomes) is called

Initial estimates of the probabilities of events are known as

If PA) = 0.50, PB) = 0.60, and PA ∩ B) = 0.30, then events A and B are

An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is

In statistical experiments, each time the experiment is repeated

From among 8 students how many committees consisting of 3 students can be selected?

A college plans to interview 8 students for possible offer of graduate assistantships. The college has three assistantships available. How many groups of three can the college select?

You are given the following information on Events A, B, C, and D. PA) = .4 PA ⋃ D) = .6 PB) = .2 PA | B) = .3 PC) = .1 PA ∩ C) = .04 PA ∩ D) = .03 a. Compute PD). b. Compute PA ∩ B). c. Compute PA | C). d. Compute the probability of the complement of C. e. Are A and B mutually exclusive? Explain your answer. f. Are A and B independent? Explain your answer. g. Are A and C mutually exclusive? Explain your answer. h. Are A and C independent? Explain your answer.

A graphical method of representing the sample points of an experiment is

A student has to take 9 more courses before he can graduate. If none of the courses are prerequisite to others, how many groups of four courses can he select for the next semester?

An experiment consists of tossing 4 coins successively. The number of sample points in this experiment is

A graphical device used for enumerating sample points in a multiple-step experiment is a