QUESTION 1

Alexa, the manager of Umbrella Corporation's primary distribution center, wants to see if there is a need to change the company's shipping partner to save money. Part of the cost of shipping its product is the distance to the customer. Another component is the time of year in which the shipments are made.

After reviewing first-quarter shipping records going back 10 years, Alexa has found the following:

• 40,863 shipments were to distances less than 150 miles away;
• 17,673 shipments were to distances from 151-600 miles away:
• 11,648 shipments were to distances over 600 miles away.

If we let the event A = (shipment distance is less than 150 miles), use the relative frequency definition of probability to find P(A) to two decimal places.

QUESTION 2      

American Bank randomly assigns six-digit PIN codes to their debit cards. Suppose your American Bank debit card is stolen and the thief wants to use your PIN to steal money from your account. The set of possible PINs is

S = {000000, 000001, 000002, . . .,999999}.

Let A be the event (first three digits of the pin are 9) and B be the event (last two digits of the pin are 9). What outcomes would be in A ∩ B?

QUESTION 3      

American Bank randomly assigns six-digit PIN codes to their debit cards. Suppose your American Bank debit card is stolen and the thief wants to use your PIN to steal money from your account. The set of possible PINs is

S = {000000, 000001, 000002, . . .,999999}.

Let A be the event (first three digits of the pin are 9} and B be the event (last two digits of the pin are 9). What is P(A ∩ B)?

QUESTION 4

American Bank randomly assigns six-digit PIN codes to their debit cards. Suppose your American Bank debit card is stolen and the thief wants to use your PIN to steal money from your account. The set of possible PINs is

S = {000000, 000001, 000002, . . .,999999}.

What is the probability that the thief guesses your pin on the first try by simply randomly guessing?

QUESTION 5

If two events A and B are mutually exclusive then the joint probability P(A and B) =

QUESTION 6

If the probability of an event A is 0.79, then the probability of A^c =

QUESTION 7

In the game of craps, you lose instantly on the first roll if you roll a sum of 2, 3, or 12, using two fair six-sided dice. Suppose you were to play the game 2 times, and each play is independent of the others, what would be the probability of losing instantly at least once in 2 plays? Hint: use the complement of the event "losing at least once" and the complement rule.

QUESTION 8

Let the experiment be rolling a fair six-sided die one time. Let A be the event that you roll an even number. Let B be the event that you roll a number greater than 2. How could the event "A or B" be represented in set notation?

QUESTION 9

Many home pregnancy tests advertise that they are 99% accurate. If we take this claim to mean that the probability that the test will detect the pregnancy hormone when it is present in urine is 0.99, what definition would the manufacturer have used to calculate this probability?

QUESTION 10

Suppose A and B are two independent events. If P(A) = 0.39 and P(B) = 0.28, what is P(A n B)?

QUESTION 11

Suppose A and B are two independent events. If P(A) = 0.45 and P(B) = 0.36. What is P(A ∪ B)?

QUESTION 12

Suppose P(A) = 0.44, P(B) = 0.41, and P (A∩B) = 0.23. What is P(A∪B)?

QUESTION 13

Suppose that the experiment is asking 3 students at SHSU what their classification is (either freshman, sophomore, junior, senior, or graduate), one after the other. How many outcomes would be in the sample space 5?

QUESTION 14

Suppose you wanted to see if a coin that you found on the ground was fair in the sense that "heads" and "tails" are equally likely. You flip the coin 100 times and record whether the outcome is heads or tails, and you decide that the proportion of times the coin lands "heads" is the probability of heads for that coin. What definition of probability are you using?

QUESTION 15

Suppose a random experiment is recording the number of days from March 31 to April 6 that it rains in Houston. List the points of the sample space, separating each point by a comma.

QUESTION 16

Umbrella Corporation has developed a new test for a disease. Before it can get government approval, it must show that the probability of having the disease, given a positive result, is high.

The company recruited a large number of individuals whose disease status (either disease free or having the disease) was known and administered the new test. The results are shown in the table below.

Find P(Has Disease I Positive). Hint: First convert all the numbers in the table to probabilities by dividing by the total of all four cells.

QUESTION 17

A university club consisting of 14 business majors, 3 criminal justice majors, 13 education majors, and 17 arts and science majors is conducting a drawing for a cash prize. Everyone in the club is eligible. Naturally, once a name is drawn, it is not replaced (the same person cannot win two scholarships).

Let E be the event a business major and a criminal justice major are drawn. Find P (E). Hint: you can think of E as the intersection of two events: A = "a business major is chosen" and B = "a criminal justice major is chosen."

QUESTION 18

Credit scores are used by financial institutions to them make decisions about to whom to grant a loan request. Many factors affect a person's score, but one of the most important is whether a person pays his or her debts back in a timely manner. The higher the score, the more likely the person is to pay his or her debts on time, or so the theory goes.

An analysis of records at a large financial institution produced the following counts related to payment behavior and credit score. Before working the problem, turn these data into probabilities by dividing each number in the table by the total number of observations.

What is the probability that, given a person has a score of 400 or more, he or she will fully repay a loan?