Exam 9: Introduction to Probability and Statistics

A college mathematics club of 30 students needs to elect new officers.If there are 3 positions available and no one can serve in more than one position,how many different slates of candidates are possible?

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.How many spending possibilities does he have?

A family is having a group picture taken to mail to all the relatives.Mother,Father,Son,and Daughter are being photographed,but somebody has to work the camera,so only 3 people at a time can be photographed.Last year's pictures looked "funny" for some reason,so this year they decide to sit next to each other in various orders to see which composition is best.Let the ordered 4-tuple (M,D,S, B) represent the photographer (Mom here), the person on the left in the picture (Dad here), the person in the middle in the picture (the Sister, in this case), and the person sitting on the right (Brother here). Determine the following events: (a) = {Dad, the tallest, sits in the middle} (b) = {the photographer is male and Mom is on the left} (c) = {there is only one female in the picture} (d) = {Dad is to the immediate left of Mom} (e) (f) ∪ (g) ∩ (h) ∩ (i) ∪ (j) ∩

Determine

Five different books are to be arranged horizontally on a bookshelf.(a)In how many ways can this be done? (b)If two are mathematics books and three are accounting books,in how many ways can all the books be arranged if the first two books are to be in mathematics?

From an ordinary deck of 52 playing cards,a two-card hand is dealt.In how many ways can the two cards be of the same face value?

If a fair die is rolled three times,find the probability that a 3 or 5 comes up each time.

A family has 3 children,2 girls and a boy.Every morning (Tuesday through Saturday)each child selects a stock at random from the list printed in the newspaper.If the stock is up,that child does the morning dishes.If the stock is down,the child who picked the stock does the noon dishes.If the stock is unchanged,that child does the evening dishes.If there is a tie-2 children to do the noon dishes,for example-then both children work together to do the noon dishes,and the remaining meal's dishes are done by default by mom or dad.The assignments can be thought of as an ordered triple,ordered by age.For example,(+,0,-)means that the youngest does the morning dishes (the stock was up),the oldest child does the noon dishes (the stock was down),and the middle child,whose stock was unchanged,does the dishes after the evening meal.(-,0,0)means the youngest does the noon dishes,the other two work together on the dishes from the evening meal.The morning dishes are done by mom and dad.Determine the following events: (a) = {the oldest and youngest work together doing the dishes; the middle child does the dishes from a different meal} (b) = {the youngest child has the day off} (c) = {mom and dad do the dishes twice} (d) = {the oldest child does the noon dishes alone} (e) (f) ∪ (g)Let = {either the oldest or the youngest child does the morning dishes alone} Let = {the middle child does the evening dishes alone} ∩ (h) ∩ (i) ∪ (j) ∩

A manufacturer of widgets has three assembly lines: A,B,and C.The percentages of total daily output that are produced by the lines are 50%,30%,and 20%,respectively.The percentages of defective units produced by the lines are estimated to be 2%,3%,and 1%,respectively.If a widget is randomly selected from a day's production and is defective,what is the probability that it came from assembly line B?

From a group of ten people,five are assigned to room A and two to room B.In how many ways can the assignment be made?

Two fair dice are rolled.What is the probability that the sum of the dots appearing is (a)2; (b)7?

If P(E)= ,P(F')= ,and P(E ∩ F) = , find P(E ∣ F).

The plane leaves on time in Chicago,given that it was late leaving New York.

A family has two children.Determine (a)the event that at least one child is a boy; (b)the event that at least one child is a girl. (c)Are and mutually exclusive?

If a basketball league has five teams,how many different end-of-the-season rankings are possible? Assume that there are no ties.

Suppose you are in a class of 20 students and the instructor randomly calls on two students to give reports.What is the probability that you will be called?

After a production run,it was found that 10% of the units produced had a faulty weld and 5% had both a defective paint job and a faulty weld.If a unit is randomly selected from this run and it has a faulty weld,what is the probability that it also has a defective paint job?

If a pair of dice are rolled,the probability that the sum of the numbers of dots appearing is 9 or 10 is

A math instructor has twelve students in his class.It so happens that he has exactly 12 desks in his classroom.How many ways can the 12 students be arranged in the 12 desks?

In a math course of 12 students,the instructor decides that he would like 4 students to go to the board simultaneously to present 4 different problems to the class.How many ways can he choose the 4 students?