Exam 3..Math

Specify the number of ways to perform the task described. Give your answers using​ P(n, r) or​ C(n, r) notation. On a biology​ quiz, a student must match fourteen terms with their definitions. Assume that the same term cannot be used twice.

(14,14). ​(Do not​ evaluate.)

Suppose that 6 cards are drawn from a​ well-shuffled deck of 52 cards. What is the probability that all 6 are clubs​?

0.000084

Assume that A and B are events. If ​P(A∪​B)=0.8​, ​P(A)=0.5​, and ​P(B)=0.45​, find ​P(A∩​B).

0.15

The windshield wipers on a car have not been working properly. The probability that the car needs a new motor is 0.55​, the probability that the car needs a new switch is 0.45​, and the probability that the car needs both is 0.15. What is the probability that the car needs neither a new motor nor a new​ switch?

0.15

Assume that the table below summarizes a survey involving the relationship between living arrangements and grade point average for a group of students. If we select a student randomly from this​ group, what is the probability that the student has a grade point average of at least​ 2.5?

0.44

The table below relates the amount of time consumers spend shopping on the Internet per month with their annual income. What is the probability that a randomly selected consumer either spends 3-9 hours per month shopping on the Internet or has an annual income below $40,000​?

0.6

The manager at the local auto shop has found that the probability that a car brought into the shop requires an oil change is 0.61​, the probability that a car brought into the shop requires brake repair is 0.39​, and the probability that a car requires both an oil change and brake repair is 0.24. For a car brought into the​ shop, determine the probability that the car will require an oil change or brake repair.

0.76

Refer to the Venn diagram to the right for events A and B in an equally likely sample space S. Find the indicated probability. ​P(A∪​B)

0.8

If the probability that an event does not occur is 0.092​, then what is the probability that the event​ occurs?

0.908

An employee at an electronics store earns both a salary and a monthly commission as a sales representative. The following table lists her estimates of the probabilities of earning various commissions next month. What is the probability that the sales representative will earn at least​ $1,000?

0.94

A town is forming a committee to investigate ways to improve public safety in the town. The committee will consist of two representatives from the seven​-member town​ council, two members of a six​-person citizens advisory​ board, and four of the 11 police officers on the force. How many ways can that committee be​ formed?

103,950

From the 6 male and 8 female sales representatives for an insurance​ company, a team of 2 men and 4 women will be selected to attend a national conference on insurance fraud. In how many ways can the team of 6 be​ selected?

1050

Seven players are to be selected from a 10​-player baseball team to visit schools to support a summer reading program. In how many ways can this selection be​ made?

120 different ways

The students in the 11​-member advanced communications design class at Center City Community College are submitting a project to a national competition. They must select a 6​-member team to attend the competition. The team must have a team leader and a main​ presenter; the other 4 members have no particularly defined roles. In how many different ways can this team be​ formed?

13,860

If the odds against event E are 3 to 17​, what is the probability of​ E?

17/20

A bag contains 6 red balls and 5 green balls. You plan to select 2 balls at random. Determine the probability of selecting 2 green balls. The problem is to be done without replacement. Use combinations to determine the probability.

2 --- 11

If eleven coins are​ flipped, what is the probability of obtaining at least one head​?

2,047 _________ 2,048

Seven players are to be selected from a 25​-player baseball team to visit schools to support a summer reading program. If they not only want to select the players but also want to assign each player to visit one of seven ​schools, in how many ways can that assignment be​ done?

2,422,728,000

How many 6​-card hands are possible with a 26​-card ​deck?

230,230

If we toss four fair​ coins, what is the probability that we get the same number of heads as tails​?

3 ___ 8

What is the probability of getting either a spade or a queen when drawing a single card from a deck of 52​ cards?

4 ____ 13

Assume you are rolling two​ dice; the first one is​ red, and the second one is green. Use a systematic listing to determine the number of ways you can roll a total of 9 on the two dice. In how many ways can you roll 9?

4 ways

Review Quiz:Review Quiz for Test 3 Question 23, *13.1-8 Test Score: 0%, 0 of 40 points Points: 0 of 1 Close Question content area top Part 1 If two fair dice are​ rolled, what is the probability that a total of six ​shows?

5 ___ 36

Use the fundamental counting principle. A password for a computer consists of six different letters of the alphabet followed by five different digits from 0 to 9. How many different passwords are​ possible?

5,012,751,744,000

If the probability that an event will occur is 611​, then the probability that the event will not occur is 511​, and the odds in favor of the event occurring are​ ________.

6:5

Of the last 60 people who went to the cash register at a department​ store, 14 had blond​ hair, 15 had black​ hair, 23 had brown​ hair, and 8 had red hair. Determine the empirical probability that the next person to come to the cash register has blond hair.

7 ___ 30

If there is a 1 in 1,000 chance that you will pick the numbers correctly in​ tonight's lottery, what is the probability that you will not pick the numbers​ correctly?

999 ________ 1000

A hot sauce bar has 15 varieties. You are going to select 3 to​ taste, but you do not care about the order in which you taste them.

C(15,3)

You are taking a​ multiple-choice test that has 8 questions. Each of the questions has 5 answer​ choices, with one correct answer per question. If you select one of these choices for each question and leave nothing​ blank, in how many ways can you answer the​ questions?

You can answer the questions in 390,625 ways.

An equestrian club has ten members. If the club wants to select a​ president, vice​ president, and treasurer​ (all of whom must be​ different), in how many ways can this be​ done?

How many ways can the three positions be​ filled? 720

List all the ways to select two different members from S without repetition. The order in which members are selected is important. For​ example, AB is not the same selection as BA. S={L, M, N, P, Q}

LM, LN, LP, LQ, ML, MN, MP, MQ, NL, NM, NP, NQ, PL, PM, PN, PQ, QL, QM, QN, QP

In order to open your garage​ door, you must enter a seven​-digit code on a keypad with numbers​ 0-9. Each number may not be used more than​ once, and the order that you enter the numbers is important.

P(10,7)

We draw a club when we select one card randomly from a standard​ 52-card deck. a. Find the probability of the given event. b. Find the odds against the given event.

a. 1/4 b. 3 to 1

Suppose the probability that a certain team will win a certain competition is 0.75. a. What are the odds in favor of the team​ winning? b. What are the odds against the team​ winning?

a. 3 to 1 c. 1 to 3

How many different​ three-digit numbers can be formed using the digits 5, 2, 6, 9, 7, and 8 without​ repetition? For​ example, 669 is not allowed.

The number of different​ three-digit numbers is 120.

How many different​ three-digit numbers can be formed using the digits 7, 2, 3, 8, 5, and 6 if repetition is​ allowed? For​ example, 338 is allowed.

The number of different​ three-digit numbers is 216.

Using the digits​ 0, 1,​ 2, ...8,​ 9, determine how many 4​-digit PIN codes are possible according to the following criteria. Zero cannot be used for the first​ digit; digits may be repeated.

The number of possible 4-digit PIN codes is 9,000

If you drew a tree diagram showing how many ways 9 different coins could be​ flipped, one after the​ other, how many branches would it​ have?

The tree diagram would have 512 branches.

A restaurant offers 7 appetizers and 9 main courses. In how many ways can a person order a​ two-course meal?

There are 63 ways a person can order a​ two-course meal.

An eyewitness to a crime said that the license plate of the getaway car began with the letters R, B, and X​, but he could not remember the order. The rest of the plate had the numbers 7 and 5​, but again he did not recall the order. How many license plates must the police investigate to find the​ car?

There are 1212 license plates for the police investigate. ​(Type a whole​ number.)