Exam 9: Introduction to Probability and Statistics

Two marbles are randomly drawn in succession without replacement from an urn that contains 10 red marbles and 10 green marbles.The probability that one marble is red and the other is green is

In a math course of 12 students,the instructor decides that he would like 4 students to go to the board to present 4 different problems to the class.The students go to the board one at a time.No student goes to the board more than once.How many ways can he choose the 4 students?

On Tuesday a store advertised a special sale for Wednesday.On Wednesday it was found that 60% of customers had known about the sale and,of these customers,40% bought a sale item.Of the customers that had not known about the sale,20% bought a sale item.If a customer bought a sale item,what is the probability that he or she had known about the sale?

The value of is

Three fair coins are tossed.Find the probability that (a)three tails show; (b)exactly two tails show.

Urn I contains three green and four red marbles,and Urn II contains one green,two white,and two red marbles.A marble is randomly drawn from Urn I and placed into Urn II.A marble is then randomly drawn from Urn II.If it is red,what is the probability that a red marble was drawn from Urn I?

A man has a $1,a $5,a $10,and a $20 bill in his billfold.He also has a penny,a nickel,a dime,and a quarter in his pants pocket.He decides to treat himself by spending one bill and one coin.Determine the following events. (a) = { the amount of money the man is prepared to spend,expressed in cents,is a prime number} (b) = {the amount of money the man is prepared to spend is more than one third of all the money he is carrying} (c) = {the man spends the nickel} (d) = {the amount to be spent is one half the amount to be spent under another selection} (e) (f) ∪ (g) ∩ (h) ∩ (i) ∪ (j) ∩

If the odds in favor of an event E are 2:7,find P(E').

Determine the value of and simplify your answer.

How many different two-card hands can be dealt from an ordinary deck of 52 playing cards?

A sample space is partitioned by events E,F,and G,where P(E)= ,P(F)= ,and P(G)= .Suppose that S is an event such that P(S∣E)= ,P(S∣F)= ,AND P(S∣G)= .Find P(E∣S).

How many distinguishable horizontal arrangements of all the letters in BOOKS are possible?

An aptitude test is believed to have 80% accuracy.Find the probability that the test will be accurate for at least one of the next two persons who take the test.

Determine the value of and simplify your answer.

Two light bulbs are selected from a box of 20 bulbs.For this experiment,how many sample points are in the sample space?

AN URN CONTAINS FOUR MARBLES,NUMBERS 1,2,3,AND 4.IF A MARBLE IS DRAWN AND THEN A COIN IS TOSSED,AND THE RESULTS are observed,determine the sample space of this experiment.

A state has decided to issue personalized license plates with 3 letters on them.The original idea was that these letters would represent the vehicle owner's first,middle,and last initials,respectively.Unfortunately,some 3 letter combinations are more colorful than others and the state received requests for combinations that in no way resembled the person's initials.The Department of Motor Vehicles decided to withdraw inappropriate or suggestive combinations.How long was the list of personalized plates that had to be reviewed?

A company will hire five people: three for the assembly department and two for the finishing department.There are eight applicants who are equally qualified to work in each department.In how many ways can the company fill the positions?

A certain state has license plates that consist of 3 letters followed by 4 numerals.How many different types of license plate can be made?

Determine