Question 1:

Employee ID numbers at a certain factory consist of one capital letter followed by a three-digit number and ending with one capital letter.

a) How many possibilities are there if repeats are allowed?

b) How many possibilities are there if NO repeats are allowed?

Question 2:

The Board of Trustees at NBCC has 10 members. Each year, they elect a 4-person committee to oversee buildings and grounds. Each year, they also elect a chairperson, vice chairperson and secretary. These selections are made from the 10 members of the Board.

a) When the board elects the buildings and grounds committee, how many different 4-person committees are possible?

b) When the board elects the 3 officers (chairperson, vice chairperson and secretary), how many different slates of candidates are possible?

Question 3:

In a class of 35 students, 25 are taking mathematics, 8 are taking history and 5 are taking both mathematics and history. If a student is chosen at random from this class, what is the probability that he or she is taking mathematics or history?

Question 4:

A research poll showed that 86% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?

Question 5:

The following are the events likely on a test and their corresponding probabilities:

A - Achieve a grade of "A"                    P(A) = .20

B - Achieve a grade of "B"                     P(B) = .15

C - Achieve a grade of "C"                     P(C) = .25

D - Achieve a grade of "D"                    P(D) = .30

F - Achieve a grade of "F"                      P(F) = .10

What is the probability of the event P, which is you pass the test (To pass a test you must have a minimum grade of "D")?

Question 6:

A statistics student wants to ensure that she is not late for an early statistics class because of a malfunctioning alarm clock. Instead of using one alarm clock, she decides to use three. What is the probability that all three alarm clocks fail if each individual alarm clock has an 92% chance of working correctly?

Question 7:

MP3 players have relatively high failure rates for a consumer product. The worst failure rate for all iPod models was the 40GB Click wheel (as reported by MacIntouch.com) at 28%. If a store sells this model and failures are independent,

a) What is the probability that the next one they sell will have a failure?

b) What is the probability that there will be failures on both of the next two?

c) What is the probability that the store's first failure problem will be the third one they sell?

d) What is the probability that the store will have a failure problem with at least one of the next five that they sell?

Question 8:

In developing their warranty policy, an automobile company estimates that over a four-year period, 17% of their new cars will need to be repaired once, 7% will need repairs twice and 4% will require three or more repairs. 

If you buy a new car from this company, what is the probability that your car will need

a) No repairs?

b) No more than one repair?

c) Some repairs?

If you bought two new cars, what is the probability that over a four-year period

d) Neither will need repair?

e) Both will need repair?

f) At least one car will need repair?

Question 9:

A board game requires players to roll a pair of dice for each player's turn. Denote the outcomes by (die 1, die 2), such as (5, 3) for a 5 on die 1 and a 3 on die 2.

a) List the sample space of the 36 possible outcomes for the two dice.

b) Let A be the event that you roll doubles (that is, each die has the same outcome). List the outcomes in A and find its probability.

c) Let B be the event that the sum on the pair of dice is 7. Find P(B).

d) Find the probability of

i) A and B

ii) A or B

iii) B given A

Question 10:

The following table shows the relationship between place of residence and ownership of a foreign car.

Car Ownership

Large City

Suburbs

Rural

Foreign

90

60

25

Domestic

110

90

125

a) If one of the 500 car owners is randomly selected, find the probability of getting a foreign car owner.

b) If one of the 500 car owners is randomly selected, find the probability of getting a foreign car owner or someone who lives in a large city.

c) If two different car owners are randomly selected, find the probability that both live in a rural area.

d) If one of the 500 car owners is randomly selected, find the probability of getting a domestic car owner who lives in the suburbs.

e) If one owner is randomly selected, find the probability of getting someone who lives in the suburbs or in a rural area.

f)  If three different owners are randomly selected, find the probability that they all own domestic cars.

g) If one owner is randomly selected, find the probability of getting a domestic car owner, given that she or he is from a large city.

h) If one car owner is randomly selected, find the probability of getting someone who lives in a large city, given that her or his car is foreign.