Probability Questions and Answers

Two dice are rolled one after the other. Construct a sample space and determine the probability that the sum of the dots on the dice total 11 if the first die is a 5. The probability that the sum of the dots on the dice total 11 if the first die is a 5 is

An experimental drug was given to a sample of 95 hospital patients with an unknown sickness. Of the total, 74 patients reacted favorably, 8 reacted unfavorably, and 13 were unaffected by the drug. Assume that this sample is representative of the entire population. If this drug is given to Mr. and Mrs. Rivera and their son Carlos, what is the probability that all three react favorably? (Assume independence.)

According to a study, 71% of K-12 schools or districts in a country use digital content such as ebooks, audio books, and digital textbooks. Of these 71%, 10 out of 20 use digital content as part of their curriculum. Find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum. The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is

A new medicine was given to a sample of 100 hospital patients. Of the total, 73 patients reacted favorably, 12 reacted unfavorably, and 15 were unaffected by the drug Assume that this sample is representative of the entire population. If this medicine is given to Mr. and Mrs. Rivera and their son Carlos, what is the probability Mrs. Rivera reacts favorably? (Assume independence.)

By rewriting the formula for the multiplication rule, you can write a formula for finding conditional probabilities. The conditional probability of event B occurring, given that event A has occurred, is P(B|A) =P(A and B)/P(A) on time. The probability that an airplane flight departs on time is 0.89. The probability that a flight arrives on time is 0.89. The probability that a flight departs and arrives on time is 0.81. The probability that a flight departed on time given that it arrives on time is (Round to the nearest thousandth as needed.) Use the information below to find the probability that a flight departed on time given that it arrives

The life expectancy (in years) of a certain brand of clock radio is a continuous random variable with the probability density function below. F(X)= {2/(x + 2)²1x20 0, otherwise (A) Find the probability that a randomly selected clock lasts at most 4 years. (B) Find the probability that a randomly selected clock radio lasts from 4 to 10 years. (C) Graph y=f(x) for [0, 10] and show the shaded region for part (A).

A single fair die is rolled twice. a) Determine the number of points in the sample space. b) Construct a tree diagram and determine the sample space. c) Determine the probability that a double (a 1, 1 or 2, 2, etc.) is rolled. d) Determine the probability that a sum of 11 is rolled. e) Determine the probability that a sum of 10 is rolled. f) Are you as likely to roll a sum of 11 as you are of rolling a sum of 10? What is the sample space? Choose the correct answer below. A. 11, 13, 15, 22, 24, 26, 31, 33, 35, 42, 44, 46, 51, 53, 55, 62, 64, 66 B. 12, 13, 14, 15, 16, 21, 23, 24, 25, 26, 31, 32, 34, 35, 36, 41, 42, 43, 45, 46, 51, 52, 53, 54, 56, 61, 62, 63, 64, 65 c. 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66 D. 11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36 c) The probability that a double is rolled is. (Simplify your answer.)

A box contains three cards. On one card there is an apple (A), on another card there is a sun (8), and on the third card there is a pear (P). Two cards are to be selected at random with replacement. Complete parts (a) through (e) below. e) Determine the probability that at most one card containing an apple is selected. The probability is . (Simplify your answer.)

A large bag of marbles contains equal amounts of each of 10 colors. Milo selects 1 marble, looks at it, puts it back, and then selects another. Find the probability of Milo selecting the same color both times.

The Triple L investment club is considering purchasing a certain stock. After considerable research, the club members determine that there is a 50% chance of making $13,000, a 10% chance of breaking even, and a 40% chance of losing $6,600. Find the expectation of this purchase.

At a homeowners' association meeting, a board member can vote yes, vote no, or abstain on a motion. There are three motions on which each board member must vote. Complete parts (a) through (e) below.

The odds in favor of Frank McKinnis winning a hot dog eating contest are 2 : 9. a. Determine the probability that Frank will win the contest. b. Determine the probability that Frank will not win the contest. a. The probability that Frank will win the contest is b. The probability that Frank will not win the contest is

If the odds in favor of Chris winning the election are 9:4, then what is the probability that a) Chris wins. b) Chris does not win. What is the probability that Chris will win the election?

Don is considering bringing a lawsuit against the Dummote Company. His lawyer estimates that there is a 60% chance Don will make $60,000, a 30% chance Don will break even, and a 10% chance they will lose the case and Don will need to pay $10,000 in legal fees. Estimate Don's expected gain or loss if he proceeds with the lawsuit. Select the correct choice below and, if necessary, fill in the answer box within your choice. A. Don has an expected gain of $ B. Don has an expected loss of S C. Don has neither an expected gain nor expected loss.

A bag contains eight batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select two batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected a) with replacement. b) without replacement.

The graph to the right is the uniform probability density function for a friend who is x minutes late. (a) Find the probability that the friend is between 10 and 20 minutes late. (b) It is 10 A.M. There is a 30% probability the friend will arrive within how many minutes? (a) The probability that the friend is between 10 and 20 minutes late is 0.333. (Type an integer or a decimal. Round to three decimal places as needed.) (b) There is a 30% probability the friend will arrive within minutes.

Assume than men's weights are normally distributed with a mean given by μ = 155 pounds and ad mont standard deviation given by o = 4.4 pounds. If one man is randomly selected, find the probability that his weight is between 152 pounds and 21 91159 pounds.

A chemistry lab requires students to identify chemical compounds by using various tests. Each student is given samples of three different compounds, labeled A, B, and C. Each student is also given a list of six possible compounds. If a student does not perform the tests and randomly chooses three from the list, what is the probability that he guesses all three correctly?

A shipment of seven smartphones contains two with cracked screens. If sold in a random order, what is the probability that the first five sold have undamaged screens?

If you toss a coin, what is the probability of it landing tails up?

There are 16 marbles in a bag; 12 of the marbles are blue and 4 are yellow. What is the probability of picking a blue marble and then a yellow marble, without replacing the first marble? a. 11/20 b. 3/7 c. 1/5

Mandy flipped a coin 50 times. The coin landed on tails 20 times. What was the experimental probability for landing on tails? A 3/5 B 2/5 C 4/5

There are 20 chocolate candies in a bag. What is the probability of reaching in the bag and pulling out a strawberry? A. 1, since all of the candies are chocolate, there is 100% chance of pulling out a strawberry B. 1/2, because half of the time you will get a strawberry C. 0, it would be impossible to pull out a strawberry because there are no strawberries in the bag

What's the probability of rolling the die twice and having it land on 5 both times? 1/36 1/6 1/3

Given the following information: P(A) = 0.37 P(B) = 0.19 P(A and B) = 0.1 P(B given A) = 0.27 What is the probability of A or B? Round your answer to the nearest hundredth as needed. P(A or B) =

What is the probability of rolling a dice and getting a 7? A. 1/6 B. 1/7 C. 0, it is impossible to roll a 7 on a dice because the dice does not have 7 on any of its sides

There are 6 red socks and 8 black socks in a drawer. Without looking, you pick out 2 socks to wear. What is the probability of picking red, black? A. 15/91 B. 14/27 C. 24/91

A spinner has the colors red, blue, and green on it. Maria spins it 30 times, and it lands on red 12 times. What is the experimental probability of spinning a red? A. 4/15 B. 2/5 C. 1/3

Tami rolled a die 20 times. 14 times it landed on an even number; 6 times it landed on an odd number. What is her experimental probability of it landing on an odd number? A. 1/2 B. 7/10 C. 3/10

There are 12 marbles in a box. 8 are purple, and 4 are green. What is the probability of picking a purple marble and then another purple marble, without replacing the first marble? A. 14/33 B. 1/11 C. 8/33

What is the probability of rolling a die, having it land on 7, and then flipping a coin and having it land on heads? A. 1/12 B. 1/2 C. 0

Theoretical probability helps us know how likely an event is to occur. Which of the following probabilities would tell us that the event is VERY LIKELY to occur? A. A probability that is close to 0, such as 1/100 B. A probability of 1/2, such as 50/100 C. A probability that is close to 1, such as 99/100

Suppose a jar contains 17 red marbles and 33 blue marbles. If you reach in the jar and pull out 2 marbles at random without replacement, find the probability that both are red.

Determine the number of outcomes in the event. Decide whether the event is a simple event or not. You randomly select one card from a standard deck of 52 playing cards. Event C is selecting a club. Event C has outcome(s). Is the event a simple event? because event C has one outcome.

A bag contains three red peppers and four green peppers. You take a pepper from the bag and eat it. You then take another pepper and eat it. a. Calculate the probability you eat two red peppers. b. Calculate the probability you do not eat a red pepper. c. Calculate the probability you eat at least one red pepper.

A math class consists of 35 students, 20 female and 15 male. Three students are selected at random, one at a time, to participate in a probability experiment (selected in order without replacement). (a) What is the probability that a male is selected, then two females? (b) What is the probability that a female is selected, then two males? (c) What is the probability that two females are selected, then one male? (d) What is the probability that three males are selected? (e) What is the probability that three females are selected?

Elizabeth brought a box of donuts to share. There are two-dozen (24) donuts in the box, all identical in size, shape, and color. Two are jelly-filled, 4 are lemon-filled, and 18 are custard-filled. You randomly select one donut, eat it, and select another donut. Find the probability of selecting a lemon-filled donut followed by a custard-filled donut.(Type an integer or a simplified fraction.)

Julian owns a small business selling ice-cream. He knows that in the last week 52 customers paid cash, 22 customers used a debit card, and 5 customers used a credit card. Based on these results, express the probability that the next customer will pay with a credit card as a fraction in simplest form.

Colton has a bag that contains orange chews, lemon chews, and peach chews. He performs an experiment. Colton randomly removes a chew from the bag, records the result, and returns the chew to the bag. Colton performs the experiment 49 times. The results are shown below: A orange chew was selected 18 times. A lemon chew was selected 6 times. A peach chew was selected 25 times. Based on these results, express the probability that the next chew Colton removes from the bag will be orange or lemon as a decimal to the nearest hundredth.

Ruby has a bag that contains orange chews, cherry chews, and lime chews. She performs an experiment. Ruby randomly removes a chew from the bag, records the result, and returns the chew to the bag. Ruby performs the experiment 42 times. The results are shown below: A orange chew was selected 4 times. A cherry chew was selected 13 times. A lime chew was selected 25 times. Based on these results, express the probability that the next chew Ruby removes from the bag will be orange or lime as a fraction in simplest form.

A bag contains six balls labeled 1 through 6. One ball will be randomly picked. What is the probability of picking a multiple of 3? Write your answer as a fraction in simplest form.

A basket is filled with 2 white eggs and 14 brown eggs. Half of the brown eggs are cracked. An egg is randomly selected from the basket. What is the probability that it is a cracked, brown egg? Write your answer as a fraction in simplest form.

Wyatt has a bag that contains pineapple chews, cherry chews, and lime chews. He performs an experiment. Wyatt randomly removes a chew from the bag, records the result, and returns the chew to the bag. Wyatt performs the experiment 33 times. The results are shown below: A pineapple chew was selected 23 times. A cherry chew was selected 6 times. A lime chew was selected 4 times. Based on these results, express the probability that the next chew Wyatt removes from the bag will be lime chew as a percent to the nearest whole number.

In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Latanya sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below. 58 visitors purchased no costume. 156 visitors purchased exactly one costume. 23 visitors purchased more than one costume. Based on these results, express the probability that the next person will purchase exactly one costume as a fraction in simplest form.

A box is filled with 5 red crayons, 9 blue crayons, and 6 yellow crayons. A crayon is chosen at random from the box. Find the probability that it is a red or a blue crayon. Write your answer as a fraction in simplest form.

A bag contains eleven balls labeled 1 through 11. One ball will be randomly picked. What is the probability of picking an even number? Write your answer as a fraction in simplest form.

Juan is going to watch a movie in his collection. He has 7 action movies, 12 comedies, and 2 dramas. He will randomly select one movie. What is the probability that the movie he selects is not an action movie? Write your answer as a fraction in simplest form.

A circular spinner is divided into 4 regions and the regions are colored blue, red, yellow, and green. Each region occupies a fourth of the circle. Suppose you decide to play a "game" with your friend. If he spins and it lands on green, you will give him $5. If he spins and it lands on any other color, he has to give you $3. What is the mathematical expectation for this game? Should your friend play with you? Your friend should play because on average he will win $1 each time he plays. Your friend should NOT play because on average he will lose $4 each time he plays. Your friend should NOT play because on average he will lose $1 each time he plays. I have no idea. When did we ever learn this?

The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with mean 264 days and standard deviation 16 days. Round all answers to the nearest whole numnber. What is the probability that a pregnancy last less than 260 days? What is the probability that a pregnancy last between 250 and 280 days? Doctors agree that serious thought to labor-producing procedures ought to accompany any pregnancy that runs in the longest 2.5% of all pregnancies. At what day should these procedures be considered?

At snack time, there were seven bags of raisins, nine bags of pretzels, and five bags of sunflower seeds. Find the probability of each situation below. Write you answer as a reduced fraction using the / symbol, ex. 1/2. a. Mara chose one bag at random and got pretzels, Since she is allergic to wheat, the teacher let her put the pretzels back, and then, she randomly chose a bag of raisins. What is the probability that she would first choose pretzels and then raisins? b. Mara completed all of her work for the week and was rewarded with two snacks. What is the probability that she chose two bags of sunflower seeds?