Probability Questions and Answers

Question spinner contains the numbers 1 through 80 What is the probability that the number that is not a multiple of 12 Give your answer in fraction form

The results from a test to detect the presence of a bacteria in a sample are shown in the table Test is positive Test is negative 68 58 126 Contains bacteria Doesn t contain bacteria Total OA OB 0 03 OC 0 46 What is the probability that the result of the test is positive given that the sample doesn t contain the bacteria 0 001 2 1 872 1 874 D 0 54 Total 70 1 930 2 000

17 During a word game Sara draws tiles at random from the group of letter tiles shown below A B B L 1 16 3 E R S C R A T T If each tile is replaced after being drawn what is the probability that Sara draws a letter from her name on the first draw and a letter not in her name on the second draw E A C D 1 2 L E T T B B E 9

Use the following scenario to solve the first four problems A card is drawn from a card deck Tell whether events A and B are inclusive or mutually exclusive and then find the probability 2 Tell whether events A and B are inclusive or mutually exclusive and then find the probability Note Do not include Aces as face cards A The card is a 10

At LaGuardia Airport for a certain nightly flight the probability that it will rain is 0 07 and the probability that the flight will be delayed is o 19 The probability that it will not rain and the flight will leave on time is 0 75 What is the probability that it is raining and the flight is delayed Round your answer to the nearest thousandth

Let in a binomial distribution consisting of 5 independent trials probabilities of exactly 1 and 2 successes be 0 4 and 0 6 respectively Then the probability of getting exactly 3 successes is equal to O 2160 74 O 4320 74 O 4320 75 O 2160 75

11 A spinner with eight congruent sectors is spun and a fair six sided die is tossed during a game A B 1 12 4 5 What is the probability of getting an even number on the spinner and a 3 on the die 2 3 1 3 2 67 1 8 C D 48

5 Broderick is playing a game where he must roll a number cube The faces of the number cube are labeled 1 through 6 If Broderick rolls a 6 on the number cube he must roll the cube again What is the probability that Broderick rolls a 6 on the number cube three times in a row A B 1 6 1 18 C D N2 1 216

In a lottery the top cash prize was 655 million going to three lucky winners Players pick four different numbers from 1 to 52 and one number from 1 to 43 A player wins a minimum award of 400 by correctly matching two numbers drawn from the white balls 1 through 52 and matching the number on the gold ball 1 through 43 What is the probability of winning the minimum award

Given the image below where the circle is tangent to two sides of the rectangle and has a radius of 3 cm The width of the rectangle is 8 cm What is the probability of choosing a point in the unshaded area Round your answer to the nearest hundredth

Refer to the following scenario and diagram below to solve the following problems A ski team with 14 members has eight 8 members who ski downhill five 5 members who ski cross country and seven 7 members who are jumpers Some skiers participate in more than one event according to the overlapping regions in the Venn diagram Find the probability of each event if a skier is selected at random Downhill 3 3 2 2 1 Cross country 2 0 Jumpers 12 does not ski cross country

The table below shows the results of a consumer survey of annual incomes in 100 households Income 0 14 999 15 000 24 999 25 000 34 999 35 000 44 999 45 000 or more What is the probability that a household has an annual income less than 25 000 OA 0 28 B 0 55 OC 0 21 Number of households 7 21 27 30 15 D 0 72

Classify the following statistic as descriptive or inferential 14 out of the 25 students taking Mr Howard s College Algebra class passed the course Descriptive

Express the probability as a reduced fraction and as a decimal rounded to the nearest hundredth A bowling alley makes a collection of bowling balls available to the public The weights in pounds are listed below If a bowler selects a ball at random find the probability that its weight is in the given range See Example 10 8 9 16 9 16 6 16 6 12 15 12 9 11 10 15 13 10 14 14 16 14 10 7 12 15 6 6 15 13 13 6 10 8 6 9 12 15 7 It weighs between 8 to 14 pounds inclusive Fraction Decimal Preview

The junior class has 50 students Twenty five students take only French 15 take only Latin and 10 take both If a student is chosen at random from the class what is the probability that the student chosen takes either French only or Latin only 01 2 O 4 5 1

A friend devises a game that is played by rolling a single six sided die once If you roll a 6 he pays you 3 30 if you roll a 5 he pays you nothing if you roll a number less than 5 you pay him 0 75 Compute the expected value for this game

Match the following items In a group of 100 persons 85 had Rh positive blood Rh factor present Rh 45 had Type O blood and 38 had both Type O and Rh positive blood If one person had been selected at random from the group what would the probability be 1 that his blood type was Type O and Rh 2 that his blood type was not O 3 that his blood type was Rh 4 that his blood type was Type O and Rh 5 that his blood type was Rh 5 that his blood type was not Type O or else was Rh 11 20 17 20 93 100 19 50 3 20 7 100

Problem 5 10 pts Ashley wants to download new music into her iPod from a list of 24 rock songs 18 rap songs and 12 alternative songs Compute the probability that a randomly selected list of 10 songs are all rap songs

Identify the sampling method for the following scenario A local restaurant manager wants to survey customers about the service they receive Each night the manager randomly chooses a number between 1 10 He then gives a survey to that customer and to every 10th customer after them to fill it out before they leave O Cluster Sample O Simple Random Sample O Convenience Sample O Systematic Sample Question 4 Identify the sampling method for the following scenario 20 pts

The table below is a result of a study for 3 000 students at Penn State University Students were grouped into two groups skipped many classes and skipped a few classes The researchers took 5 SRS s and found their average GPA GPA for a Few Classes Skipped 3 5 3 2 3 0 3 3 3 6 GPA for Many Classes Skipped 3 4 2 9 2 5 3 0 2 75 Difference 0 1 0 3 0 5 0 3 0 85 After finding the differences between the GPA GPA for Few Classes Skipped GPA for Many Classes Skipped what conclusion can you make from the table Since all of the differences were small we cannot conclude that on average skipping many classes affects GPA Since all of the differences were positive we can conclude that on average students that skip less classes have a higher GPA than students who skip many classes No conclusion can be made from the table More data needs to be collected Since all the differences were negative we can conclude that on average students that skip less classes have a lower GPA than students that skip many classes

56 Tasha is in the science club There are 21 students in the club Two of them will be picked at random to attend an awards banquet What is the probability that Tasha will not be randomly chosen to attend the banquet

7 On the dart board the center circle has a diameter of 2 inches What is the probability of hitting the shaded ring Round to the nearest hundredth A 0 01 B 0 29 C 0 30 D 0 45 11 5 in 5 in keb

A high school gym teacher randomly selects a group of two players from three students to demonstrate a basketball drill during class The three students consists of two girls Andrea and Marta and one boy Davi The sample space of possible groups is listed below Let A be the event that the first player the coach chooses is a girl and B be the event that the second player is a boy What is P A or B the probability that the coach chooses a girl first or a boy second Group 1 Andrea Group 2 Andrea Group 3 Group 4 Group 5 Marta Marta Davi Marta Davi Andrea Davi Andrea

Question Mary wanted to track the growth of various peppers in her garden so she decided to label them Her garden had RED peppers labeled 1 2 3 4 5 6 GREEN peppers labeled 1 2 3 4 5 and YELLOW peppers labeled 1 2 If a single pepper is picked at random what is the probability that the pepper is YELLOW AND has an ODD number Provide the final answer as a fraction quide your answer below

The offices of president vice president secretary and treasurer for an environmental club will be filled from a pool of 18 candidates Eight of the candidates are members of the debate team a What is the probability that all of the offices are filled by members of the debate team b What is the probability that none of the offices are filled by members of the debate team a P all offices filled by debate team members Round to three decimal places as needed b P no offices filled by debate team members Round to three decimal places as needed

The names of 3 boys and 5 girls are written on cards The cards are placed in a bowl Two cards are drawn one at a time without replacement What is the probability that the first card is a girl s name and the second card is a boy s name O A 1 56 OB 5 15 O C 15 56 OD 1 15

A store purchases baseball hats from two different manufacturers in 3 different colors summarized below One hat is chosen at random Black Blue Red Total 22 11 16 49 13 18 26 57 35 29 42 106 a Find the probability that the hat was Red or was from Manufacturer A Manufacturer A Manufacturer B Total b Find P Red

3 A group of students were asked if they play a sport or play an instrument The results are shown in the Venn diagram below If one of these students is chosen at random find each probability a P instrument b P does not play a sport Instrument Sport c P both instrument and a sport d P sport but not an instrument

A die is rolled and a spinner like the one at the right is spun Find each probability A 7 P 4 and A C 8 P an even number and C worl2 slun steniboos brit nevig smugit and to sgomi eny ov y x a X 9 P 2 or 5 and B or D 10 P a number less than 5 and B C or D x x

7 A brand of jeans comes in nine different washes five different fit styles and three different height options If two of the wash options are out of stock how many ways can someone order a single pair of jeans A 95 B 105 C 120

A student picks a random letter from the word cat and a random letter from the word meow Express answers that are not whole numbers as fractions a How many outcomes are in the sample space b What is the probability that a C is chosen c What is the probability that a W is chosen d What is the probability that a C and W are chosen

A spinner has 8 equally sized sections 2 of which are gray and 6 of which are blue The spinner is spun twice What is the probability that the first spin lands or blue and the second spin lands on gray Write your answer as a fraction in simplest form 0 00

Question 5 1 pts Nine hundred 900 high school freshmen were randomly selected for a national survey Among survey participants the mean grade point average GPA was 2 7 and the standard deviation was 0 4 What is the margin of error assuming a 95 confidence level round to the nearest thousandths place

Consider the following table with information about a sample of students from GCA and if they had trigonometry before taking AMDM If a person is randomly selected determine the following probability provided the conditions P Trig Male No Tng Total Female Male Total 2 11 1 6 11 24 1 3 Trig 14 8 22 10 16 26 24 24 48

A distribution is given as X U 0 12 Find P x 3 Enter an exact number as an integer fraction or decimal

Experiment You roll a die P 4 P 4 not 6 P 4 even P 4 greater than 2 P 4 less than 4 9 10 11 12 13 14 15 16 17 18 P odd P odd prime P odd 3 P odd even P odd greater than 1

Moe plays a simplified version of powerball You either win the entire jackpot of 500 000 000 or you lose the cost to play i e 2 The probability of winning powerball is 1 out of 292 201 338 the probability of losing is thus 1 292 201 338 What is the expectedyolu

2 A group of 140 high school students were asked Do you play a musical instrument The results are shown in the table below F G 43 140 Males Females 43 67 Survey Results If a musician is selected at random what is the probability that the individual is a female student 43 75 Play a musical instrument 24 43 H J Do not play a musical instrument 15 28 41 32

Sales representatives at a car dealership were split into two groups One group used an aggressive approach to sell a customer a new automobile The other group used a passive approach The following table summarizes the records for 646 customers If one of these customers is selected at random determine the probability that the passive approach was used P Approach Aggressive Passive Total Sale 109 201 310 No Sale 246 90 336 The probability that the passive approach was used is Type an integer or a simplified fraction Total 355 291 646

This is a 2 page document Directions Find the total number of outcomes that are possible 1 The spinner below is spun three times 17 3 3 Selecting a letter from the word TROPHY and a day from the month of May 3 3 X6 2 5 Creating a password with two letters followed by two one digit numbers Z 2X2 c P factor of 72 and even 2 A bag contains 5 green marbles and 8 blue marbles A dice is rolled then a marble is chosen at random from the bag B3X6 4 Jaden is studying abroad for a semester 2 He can choose the first semester or second semester then choose France Spain Germany Italy or Japan 245 7 A number from 1 72 is chosen at random Find each probability as a fraction in simplest form decimal and percent a P multiple of 9 b P odd or at most 16 c P face card or 8 6 A coin is tossed four times and a card is 52 selected from a standard deck of cards 524 d P not a perfect square 52 8 A card is chosen at random from a standard deck Find each probability as a fraction in simplest form decimal and percent a P ace b P black or queen d P red jack Gina Wilson All Things Algebro LLC 2020

What is the probability that out of 175 chicks hatched on Peeper Farm at least 70 will be female Assume that males and females are equally probable and round your answer to the nearest tenth of a percent O A 3 5 B 99 7 XO C 88 7 O D 38 1

George believes the Art Club students at his school have an unfair advantage in being assigned to the art class they request He asked 500 students at his school the following questions Are you in the Art Club and Did you get the art class you requested The results are shown in the table below Art Club Not in Art Club Total Received art class requested Did not get art class requested 65 Total 165 100 265 70 335 365 135 500 Help George determine if all students at his school have an equal opportunity to get into the art class they requested Show your work and explain your process for determining the faimess of the clar

In a class of 26 students 17 have a brother and 12 have a sister There are 5 students who do not have any siblings What is the probability that a student has a brother given that they have a sister

At a school s open house T shirts and sweatshirts were sold Each item was purchased by either a student or a parent The two way frequency table summarizes a random sample of 50 items sold that night Student Parent T shirt 12 18 Sweatshirt 11 9 Let student be the event that an item randomly chosen from among those sold was purchased by a student Let T shirt be the event that an item randomly chosen from among those sold was a T shirt Find the following probabilities Write your answers as decimals If necessary consult a list of formulas a P T shirt 0 24 b P student and T shirt 0 82 NUME c P student T shirt

Use for questions 9 12 A group of students were asked if they have at least one sibling and at least one pet Of the students surveyed 27 said they have a sibling and 24 students said they have a pet Of the students who said they had a sibling 12 do not have pets 9 Complete the Venn diagram to the right to represent the results of this survey 11 P does not have a pet Sibling If one of these students is chosen at random find each probability as a fraction in simplest form 10 P has a sibling and a pet 12 P has a pet but no sibling 10 11 Pet 12

4 Out of 75 students 45 are taking Algebra 2 and 32 are taking Chemistry Sixteen students are taking both Algebra 2 and Chemistry If a student is chosen at random what is the probability that the student is taking Algebra 2 but not Chemistry

Juan runs a company that makes pens He notices that 1 out of every 9 pens are faulty He uses a standard deck of cards to model the situation with all the 10s representing faulty pens Which statement about his model is true OA His model cannot be improved O B His model can be improved the most by removing all the hearts from the deck O C His model can be improved the most by removing all face cards from the deck O D His model can be improved the most by removing all the face cards and aces from the deck

Directions Find each binomial probability 5 The probability that Ashley wins a race against Madelyn is 25 What is the probability that Ashley wins exactly three of the next five races against Madelyn

A multiple-choice test has six possible answers for each question. (a) If a student guesses at the answer, what is the probability that he or she selects the correct answer for one particular question? (b) If the student first eliminates one of the six possible answers and guesses from the remaining possibilities, what is the probability that he or she selects the correct answer to that question? (a) If a student guesses at the answer, the probability that he or she selects the correct answer for one particular question is (Type an integer or a simplified fraction.) (b) If the student first eliminates one of the six possible answers and guesses from the remaining possibilities, the probability that he or she selects the correct answer to that question is (Type an integer or a simplified fraction.)

What is the probability that a card drawn randomly from a standard deck of 52 cards is a six? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth. Choose the correct answer from the options below. 1/4= 0.25 1/13≈ 0.076923 1/26≈ 0.038462 1/52≈ 0.019231