Probability Questions and Answers

You are ordering three boxes colored red, orange, and blue from left to right. What is the probability that the box on the left is orange, and the middle one blue? 1/3 1/6 1/2 2/3

There are 16 nominees in the 2021 Rock and Roll Hall of Fame class. 11 of them began their recording careers prior to 1985. 6 of these nominees will be selected as a winner and honored as Hall of Fame members. Assume each nominee has the same change of being selected as one of the winners. If a group of 6 winners is selected, find the probability that exactly 4 of the new inductees began their recording careers prior to 1985.

A hotel has four elevators. One of them is a freight elevator. When pressing the button, one of the elevators randomly services your floor. If you use the elevators seven times, what is the probability that you use the freight elevator exactly four times?

On the back of most credit cards is a three-digit Card Verification Code (CVC). If the credit card companies are considering using letters A-Z and numbers 0-9 to improve security, what is the approximate probability that two of the digits are numbers? 0.056 0.20 0.0023 0.0168

Seven students are selling candy bars to raise money for a school trip. Assume all students have an equal chance of selling the greatest number of candy bars. What is the probability that Tyrone will sell the most candy bars five weeks in a row? (1/7)5 1/7 (1/5)7 1/5

Twenty students entered an art contest, at which first, second, and third prizes would be given. If the same students entered the contest four years in a row, what is the chance that Ann would be first, Bob second, and Carlos third all three years? Assume equal chance of any student winning or not winning any award. (1/6,840) ³ (1/1,140) ³ 1/1,140 1/6,840

A deck of cards consists of ten red, ten blue, ten yellow, and ten green cards. If five cards are selected, find the probability of selecting four red cards and one other card. 252/658,008 175/18,278 7/18,278 175/18,278 1/18,278 5/82,251

Alex and Brian play a game three times, during which each has an equal probability of winning. What is the probability that Brian will win at least one game? 0.875 0.75 0.25 0.125

The probability that a tornado will hit Town D in any given year is 0.05. If A is the event that a tornado hits Town D in a given year, what is the probability that at least one tornado will hit Town D over the course of ten years? 0.40 0.95 0.60 0.50

The probability that it will rain on October 24 Is 0.13. What is the probability that it will rain five years in a row on October 24? 0.0000371 0.13000 7.00000 0.000287

A deck of twelve cards consists of five green cards, four purple cards, and three yellow cards. What is the probability of being dealt a hand with two green cards, two purple cards, and one yellow card? 18/792 60/792 180/792 360/792

Common test generators have the writer provide four possible answers. Then the test generator creates different versions of the test, randomly assigning the correct answer to a letter. There are five multiple choice questions with options (A, B, C, and D) on a qulz. What is the probability the first three answers are C? 1/1,024 5/1,024 1/64 5/256

There are two administrators, eight faculty, and six staff members for a committee. If a subcommittee of four is formed, what is the probability of selecting one administrator, two faculty, and one staff member? 12/1,820 56/1,820 168/1,820 336/1,820

An online account provides a randomly generated PIN consisting of digits from zero to nine. The digits can be repeated. What is the probability all four digits being the same? 1/10 1/100 1/1,000 1/10,000

The probability of rain for March 13 is 0.35. What is the probability that it will on March 13 for four years in a row? 0.3500 0.1225 1.400 0.0150

In a factory that has been accident-free for a month, the employees enter a drawing to win gift cards. If the same five workers are in the drawing each month, what is the probability that Sam and Janelle win a gift card for four consecutive months? (1/10)4 (1/20)4 1/20 1/10

Five years after 650 high school seniors graduated, 400 had a college degree and 310 were married. Half of the students with a college degree were married. What is the probability that a student does not have a college degree or is married? 31/65 56/65 5/13 9/13

The Robotics Club at Wickliffe High School has sixteen members of whom five are seniors, six are juniors, three are sophomores, and two are freshmen. What is the probability that three of the members selected at random are two seniors and one freshman?

There are ten teachers and sixty students in the student government of a high school and only five people are chosen to be on the committee. Which of the following shows the probability of selecting five students? 60C5/70C5 10C5/70C5 60P6/70P6 60P5/60P60

You are setting up a trophy display with eight out of twelve trophies for your school. Any trophy can fit anywhere in the display, but the principal has Instructed you to put the four first place trophles In four specific spots. What is the probability that placing the trophles at random would work? 1/32,760 1/11.880 1/35,640 1/1,320

We are ordering two out of three boxes colored red, green, and blue from left to right. What is the probability that the box on the left is green? 1/3 1/6 1/2 1/4

You select four fruits at random from a pile with half grape bunches and half banana bunches. If X Is the number of grape bunches that appear, what is the mean of the probability distribution?

A charity group has a raffle where fifty tickets are handed out. Six members of a family each receive a ticket. If there are three prizes awarded, what is the probability the family wins all prizes? 1 / 19,600 10 / 19,600 20 / 19,600 40 / 19,600

There are ten color cholces for a car. The other cholces are with or without a sunroof, with or without a spoller, and with or without leather seats. What is the probability that the next customer will select a car of any color with all of the options (a sunroof, a spoller, and leather seats)? Assume that each option is equally likely to be chosen. 1/10 1/8 5/16 5/8

A survey of 200 people included 90 females. It found that 60 people smoked, 40 of whom were male. Use the given information to complete a table: if a person is selected at random, find the probability that this person is: a) a female non-smoker b) a male given the person was a non-smoker. c) Male d) Smoker e) Smoker given that she is female f) are the events independent?

A pair of number cubes Is rolled once. What Is the probability of rolling doubles? Assume the number cubes are fair. 1/36 1/18 1/6 1/2

You bought seven different frults at the grocery store and are setting five of them on the kitchen counter at home. What Is the probability that the first three are orange, peach, banana? 1/210 1/420 1/630 1/1,200

A coin is flipped four times. What is the probability of getting four heads? Assume the coln is equally likely to land on a head versus a tail.

You are pulling four marbles of different colors out of a bag. What is the probability that the first one will be red and the second green? 1/12 1/4 1/8 1/24

The options for a dessert are chocolate, vanilla, and strawberry Ice cream, with chocolate, strawberry, and caramel toppings. What is the probability that vanilla Ice cream with strawberry topping is selected? Assume that each flavor Is equally likely to be chosen. 1/12 1/9 1/6 1/3

44% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) a least four, (c) less than eight. (a) P(3)= (Round to three decimal places as needed.) (b) P(x24)= (Round to three decimal places as needed.) (c) P(x<8)= (Round to three decimal places as needed.)

In the example of rats playing musical chairs, how would the probability of a certain rat being in a certain chair change in the case of five rats and four chairs, compared to five rats and five chairs? A fifth chair or no chair makes no difference for calculating the probability. The probabilities are only different if there is only one chair. The probability would become greater; there are fewer chairs. The probability would become less; there are fewer chairs.

In a survey of women in a certain country (ages 20-29), the mean height was 65.4 inches with a standard deviation of 2.77 inches. Answer the following questions about the specified normal distribution. (a) What height represents the 95th percentile? (b) What height represents the first quartile? (a) The height that represents the 95th percentile is inches. (Round to two decimal places as needed.) (b) The height that represents the first quartile is inches. (Round to two decimal places as needed.)

Max sleeps in 4 out of 5 days in a week. If he wakes up late, the probability that he's late for school is 9/10. If he doesn't wake up late, the probability he's late for school Is 3/10. What percent of days does he get to school on time? 11/50 13/50 22/50 7/10

A box has four cards numbered 1, 2, 3, and 4 Rafael will toss a coin once and record the toss as heads (H) or tails (T). Then he will randomly pick a card from the box and record the number chosen. Give the sample space describing all possible outcomes. Then give all of the outcomes for the event that the number chosen is 3.

Bag A contains 10 marbles of which 4 are red and 6 are black. Bag B contains 12 marbles of which 8 are red and 4 are black. A ball is drawn at random from each bag. What is the probability that you draw red marbles from both bags?

Suppose that a family has 4 children. If the probability of having a girl Is 0.5, which simulation could be used to simulate the probability of having all girls? What is the theoretical probability of having all girls? Let H represent having a girl and T represent having a boy; 4 heads; \P\left(k-4\right)=\frac{41(4Neft(O\right)!\times0.5^40.5^0) Let H represent having a girl and T represent having a boy; 4 tails; Let T represent having a girl and H represent having a boy: 1 tail and 3 heads; \P\left(k-1\right)=\frac[4!) 10.5^3\) [1Meft(3\right)!\times0.5 \P\left(k-4\right)=\frac[41X4Neft(O\right)\times0.5 40.5^0) Let T represent having a girl and H represent having a boy; 2 heads and 2 tails; VP\left(k-2\right)=\frac{2} (2Neft(2\right)!\times0.5^20.5^2)

In a neighborhood with 1,269 homes, the exterior of each home must be painted with one of only six colors - white, yellow, grey, blue, green, or brown. There are 234 homes painted white, 125 homes painted yellow, 433 homes painted grey, 207 homes painted blue, 98 homes painted green, and 172 homes painted brown. If a home is randomly selected for an Inspection, what is the probability Is It painted brown? 0.1355 0.1844 0.1720 0.2692

The probability of a sunny day is 3/7 and the probability of a rainy day is 4/7. If It's a sunny day, the probability Paul cycles to work is 7/10, the probability he drives to work is 2/10, and the probability he takes the train to work is 1/10. If It's a rainy day, the probability Paul cycles to work is 1/9, the probability he drives to work is 5/9, and the probability he takes the train to work is 3/9. What is the probability Paul bikes, regardless of the weather today? 0.36 0.48 0.52 0.32

Say that a game consists of two steps. First, you roll a die. If you roll a 1 or a 6, you continue; otherwise, you lose the game. If you rolled a 1 or a 6 and can continue playing the game, the second step is to draw a random card from a standard deck of 52 playing cards. If you draw an ace or a 6, you win. What is the probability that you will win this game? 2/39 1/3 8/52 19/39

A spinner is used for which it is equally probable that the pointer will land on any one of eight regions. One of the regions is colored blue, four are colored purple, and three are colored brown. If the pointer is spun once, find the probability it will land on brown and then purple. 7/8 3/16 1/8 3/4

Your little sister is selling scout cookles and you go along with her. Suppose the probability that a person answers the door is 0.4. What is the probability that your first opened door Is at the third house? 0.144 0.240 0.864 0.096

In a sample of 40,000 first-born babies, 7 were found to have a certain syndrome. Find the empirical probability that a family's first child will be born with this syndrome. The empirical probability is.

A shuttle bus arrives at a hotel every 40 minutes to take guests into town. If a guest walks out the door at a random time, find the probability of each waiting time. a) P(at least 15 min) b) P(no more than 10 min)

Kyla bought a raffle ticket at a charity event. Five raffle ticket winners are chosen every 45 minutes. If Kyla steps out to take a phone call at a random time, what is the probability that she has at least 10 minutes before winners are called again? A. 22.2% B. 77.8% C. 66.7% D. 75%

Suppose the probability that a basketball player makes a foul shot (the probability of success) Is 0.35. Would you use a binomial distribution or geometric distribution to determine the probability that the basketball player makes the first foul shot on the fifth attempt? What is that probability? binomial; 0.010 geometric; 0.010 binomial; 0.062 geometric; 0.062

The probability of an employee at a large company being out sick on any given day is 0.08, and the probability of an employee at a large company being out sick and there being a fire drill on any given day is 0.0004. a. Find the probability of there being a fire drill given that an employee is out sick. b. If the probability of there being a fire drill is .005, what can you conclude?

You bought an appliance and the salesperson offered you a warranty that costs $99 a year. You did some research and found that the average cost of a repair for your appllance Is $500. Which statement is true? Using your knowledge of probability and expected value, you decide you are more likely to come out ahead if you buy the warranty. Using your knowledge of probability and expected value, you decide your best option is to refuse the warranty. A person who uses the item more frequently than you is less likely to benefit from the warranty. It is never a good decision to buy a warranty.

The probability that a randomly chosen American household owns a gun is 0.43 (source). The probability that a randomly chosen American household owns a microwave is 0.968. Assuming that these events are independent, what is the probability that a randomly chosen American household owns neither a gun nor a microwave? 0.0182 0.0223 0.0514 0.3980

A local club plans to host a tennis tournament. The club will Invest $12,000 and hopes to sell tickets worth $18,000. The weather forecast Is a 20% chance of rain. If It does rain, the tournament will be cancelled, and the club will lose all of its Investment. Do you think this is a good Idea? Find the expected value of hosting the tournament. $6,000 $2400 $12,000 $8,400