Probability Questions and Answers

2. Given A, B and C are mututally exclusive and exhaustive events with p(A)=0.3, p(B)=0.5, and p(C)=0.2. For an event G, we know that p(G|A)=0.8, p(G|B)=0.7, and p(G|C)=0.9. Find p(G).

A group consists of 6 men and 5 women. Four people are selected to attend a conference. In how many ways can 4 people be selected from this group of 11? In how many ways can 4 men be selected from the 6 men? Find the probability that the selected group will consist of all men.

Find the probability. A bag contains 9 red marbles, 3 blue marbies, and 4 green marbles. What is the probability of choosing a blue marble when one marble is drawn?

Given the following information: P(A) = 0.58 P(B) = 0.46 P(A and B) = 0.44 P(B given A) = 0.76 What is the probability of A or B? Round your answer to the nearest hundredth as needed.

Provide an appropriate response. Express your answer as a simplified fraction unless otherwise noted. If P(A) = 0.45, P(B) = 0.25, and P(B|A) = 0.45, are A and B independent? yes cannot determine no

You roll two standard 6-sided dice at the same time. What is the probability that the sum of the dice is not 8? Express your answer as a fraction in simplest terms. 31/36 13/18 1/6 5/36

Zach scores a ringer 40% of the time that he throws a horseshoe. Let R be the number of throws it takes Zach to score his first ringer in a game. Assume the results of each throw are independent. Find the probability that it takes Zach 2 or fewer throws to score his first ringer. You may round your answer to the nearest hundredth. P(R≤ 2) =

Determine if the following probability experiment represents a binomial experiment. A random sample of 15 middle school students is obtained, and the individuals selected are asked to state their heights. Choose the correct answer below. A. No, this probability experiment does not represent a binomial experiment because the trials are not independent. B. Yes, this probability experiment represents a binomial experiment because the probability of success is the same for each trial of the experiment. C. No, this probability expe Question Viewer represent a binomial experiment because the variable is continuous, and there are not two mutually exclus outcomes. D. Yes, this probability experiment represents a binomial experiment because each trial has two mutually exclusive outcomes.

A jar contains 5 pennies, 5 nickels and 6 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Round your answers to 3 decimal places. Find the probability X = 10. Find the probability X = 11.

A radio station runs a promotion at an auto show with a money box with 14 $100 tickets, 11 $50 tickets, and 13 $25 tickets. The box contains an additional 20 "dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that exactly two $100 prizes and no other money winners are chosen. The probability that exactly two $100 prizes and no other money winners are chosen is (Round to four decimal places as needed.)

A radio station runs a promotion at an auto show with a money box with 11 $100 tickets, 15 $50 tickets, and 15 $25 tickets. The box contains an additional 20 "dummy" tickets with no value. Three tickets are randomly drawn. Find the probability that all three tickets have no value. The probability that all three tickets drawn have no money value is (Round to four decimal places as needed.) .....

A shipment of 9 computers contains 4 with defects. Find the probability that a sample of size 4, drawn from the 9, will not contain a defective computer The probability is (Type an integer or a simplified fraction.)

A study reports that 61% of Americans support increased funding for public schools. If 3 Americans are chosen at random, what is the probability that: a) All 3 of them support increased funding for public schools? b) None of the 3 support increased funding for public schools? c) At least one of the 3 support increased funding for public schools?

First, we need to test whether the two events are independent. Use X to denote the event described by "A person used Brand X," and G to describe the event "A person gave up doing laundry." Recall that the two events are independent if and only if the probability of GnX is equal to the product of the probabilities of X and of G. That is, if and only if P(GMX) = P(G)- P(X). To answer the question, calculate P(G), P(X), and P(GNX) and then compare P(GNX) to P(G)- P(X). Because 6% of the population gave up doing laundry, the probability that someone quit doing laundry is P(G) = 0.06. Similarly, 70% of the population used Brand X, so the probability that someone was a Brand X user is P(X) = Furthermore, 7% of the population used Brand X and then gave up doing laundry, so the probability that someone was initially a Brand X user and then quit doing laundry is P(Gnx) =

WANEFMAC7 8.2.047. MY NOTES ASK YOUR TEACHER PRACTICE ANOT A random sampling of chicken in supermarkets revealed that approximately 70% was contaminated with an organism. Of the contaminated chicken, 20% had the strain that is resistant to antibiotics. Construct a relative frequency distribution showing the following outcomes when chicken is purchased at a supermarket: U: the chicken is not infected with the organism; C: the chicken is infected with the nonresistant organism; R: the chicken is infected with the resistant organism. P(U) = 0.1 P(C) = 0.2 P(R) = 0.7 Need Help? X X X Read It ANSWERS ☆

In a brand recognition study, 1105 consumers knew of Exxon, and 41 did not. Use these results to estimate the probability that a randomly selected consumer will recognize Exxon.

An American roulette wheel has 38 slots: two slots are numbered 0 and 00, and the remaining slots are numbered from 1 to 36. Find the probability that the ball lands in an odd-numbered slot (not including 0 or 00). Your answer is:

If P(E)=0.23, find the odds against E. What are the odds against E? Select the correct choice below and fill in the answer box(es) to complete your answer. A. The odds are ___ to ___ The odds are

A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 101.3°F. Among other data, the researchers obtained the body temperatures of 95 healthy animals. Suppose you want to use those data to decide whether the mean body temperature of healthy animals is greater than 101.3°F. Complete parts (a) through (c) below. a. Determine the null hypothesis. H0: µ (Type an integer or a decimal. Do not round.)

Estimate the sample size needed if no estimate of P is available. A sample of operations is needed to obtain a 99% confidence interval with a margin of error of 0.07 when no estimate of p is available

Akira wants to purchase his first new car and can select one option from each category. Engine Type Color Hybrid Bunt copper Cobalt blue Meta coreen Draw a tree diagram to determine the sample space and find the probabilities. Model Ford Focus Honda CivIC Part 1 of 6 Find the sample space for all possible choices. For the car model, FF means Ford Focus and HC means Honda Civis means E-85; for color, BC means burnt copper, CB means cabalt blue, and MG means meta c green. OFFHBC, FFHCB, FFHMG, HCHBC, HCHCB, FFHMG, TCHBC, TCHCB, TCHMG) (FFHBC, FFHCB, FFHMG, FFEBC, FFECS, FFEMG, HEHBC, HCHC3, HC-MG, "CEBC. HCECB, HCEMG) (FFBC. FFCB, FFMG, FFE, FFH, HCBC, HCCB, HOME, HCE, HCH. TCBC, TCCB, TCMG. TCE, TCH) (FFHBC, FEHCB, FFHMG, FFBCH, FFBBC, FFECE, HCBCE, HCHBC, HCHCB, ACHMG, HCBCH, HCEBC HCECB, FFEMG, HCBCE, TCHBC, TCHCB, SCHMG, TCBCH, TCEBC, TCECB, TCENG, TCBCE

Which of the following choices can be considered binomial random variables? Choose all answers that apply: B Roll a fair die 5 times and let X the number of rolls that land showing a "4". Roll 5 fair dice at once and let Z = the number of dice that land showing an even value (2, 4, or 6). Roll 5 fair dice at once and let Y = the number of dice that land showing a "4".

After a late night of studying, Ebony decides to grab a latte before class so she can stay awake through her morning lecture. She has five-dollar bill, and a ten-dollar bill in her wallet. She pulls one out and looks at it, but then she puts it back. Distracted by a flyer for a organization, she randomly hands a bill from her wallet to the clerk. Construct a sample space, and find the probability that (a) Both bills have the same value. (b) The second bill is smaller than the first bill. (c) The value of each of the two bills is even. (d) The value of exactly one of the bills is odd. (e) The sum of the values of both bills is less than $5, Write your answers in exact, simplified form.

7. [-/1 Points] DETAILS Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. HINT [See Example 1.] The sum is 3, given that the green one is either 2 or 1. Need Help? WANEFMAC7 8.5.018. Read It

Data on salaries in the public school system are published annually by a teachers' association. The mean annual salary of (public) classroom teachers is $58.9 thousand. Assume a standard deviation of $8.4 thousand. Complete parts (a) through (e) below. a. Determine the sampling distribution of the sample mean for samples of size 64. The mean of the sample mean is μ = $58,900. (Type an integer or a decimal. Do not round.) The standard deviation of the sample mean is o = $ 1050. (Type an integer or a decimal. Do not round.) b. Determine the sampling distribution of the sample mean for samples of size 256. The mean of the sample mean is µ = $ 58900. (Type an integer or a decimal. Do not round.) Ⓒ The standard deviation of the sample mean is o = $525. (Type an integer or a decimal. Do not round.) c. Do you need to assume that classroom teacher salaries are normally distributed to answer parts (a) and (b)? Explain your answer. OA. Yes, because x is only normally distributed if x is normally distributed. OB. No, because if x is normally distributed, then x must be normally distributed. C. No, because the sample sizes are sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x. OD. Yes, because the sample sizes are not sufficiently large so that x will be approximately normally distributed, regardless of the distribution of x. d. What is the probability that the sampling error made in estimating the population mean salary of all classroom teachers by the mean salary of a sample of 64 classroom teachers will be at most $1000? (Round to three decimal places as needed.)

A drawer contains 40 socks, out of which 20 are red, 5 are blue and 15 are green. A sock is drawn from it without looking. and then put back. The process is then repeated for another sock. What is the probability that the socks are both green? Give the answer rounded to three decimal places. .375 CH

Consider the following. A die is rolled 70 times with the following result: 1 and 2 never come up, 3 and 4 each come up 25 times, and 5 and 6 each come up 10 times. E is the event that the number that comes up is at least 4. Determine the following values. fr(E) N = Calculate the relative frequency P(E). (Round your answer to two decimal places.) P(E) =

The modeling and solution of problems concerning motel reservation networks for motels were studied. Researchers defined a Type I call to be a call from a motel's computer terminal to the national reservation center. For a certain motel, the number, X, of Type 1 calls per hour has a Poisson distribution with parameter λ = 1.5. Complete parts (a) through (e) below. a. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be exactly four. b. Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be at most two.

The probability is 0.3 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In six traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a. exactly three; at least three; at most three. b. between two and four, inclusive. c. Find and interpret the mean of the random variable Y. d. Obtain the standard deviation of Y.

A packet of gummy candy contains two strawberry gums, four lime gums, four black currant gums, and two orange gums. April May sticks her hand in and selects six at random. Complete th following sentences. (a) The sample space is the set of all sets of gummy candies chosen from the packet of PRACTICE ANO (b) April is particularly fond of combinations.of.two.strawberry and four black currant gums. The event that April will get the combination she desires is the set of all sets of ✓and ---Select--- gummy candies in which ---Select--- ---Select---

The probability is 0.4 that a traffic fatality involves an intoxicated or alcohol-impaired driver or nonoccupant. In ten traffic fatalities, find the probability that the number, Y, which involve an intoxicated or alcohol-impaired driver or nonoccupant is a. exactly three; at least three; at most three. b. between two and four, inclusive. c. Find and interpret the mean of the random variable Y. d. Obtain the standard deviation of Y.

Consider the following. HINT [See Examples 1-3.] Two indistinguishable dice are rolled; both numbers are prime. (A positive integer is prime if it is neither 1 nor a product of smaller integers.) Which of the following sets of elements are included in the sample space? (Select all that apply.) O (5,5) (5,6) (5,7) (3,3) (3,4) (3,5) (3,6) (3,7) □ (4,4) (4,5) (4,6) (4,7) □ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (1,7) (6,6) □ (7,7) (6,6) (6,7) □ (4,4) (4,5) (4,6) □ (3,3) (3,4) (3,5) (3,6) (2,2) (2,3) (2,4) (2,5) (2,6) (2,7) □ (5,5) (5,6) (2,2) (2,3) (2,4) (2,5) (2,6) □ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) List the elements of the given event. (Select all that apply.) □ (2,2) ☐ (5,7) ☐ (2,5) ☐ (5,4) □ (2,4) □ (2,7) =27692990&tags=autosave#question3772294_4 (3,7) (5,5) (3,4) (3,5) (3,3) □ (2,3) 3 43 F

To choose the order of bands for the finals of a Battle of the Bands competition, Freddy puts a penny, a nickel, a dime, a quarter, and a half-dollar into five separate envelopes and has one band choose an envelope. The second band then chooses from the remaining envelopes. Draw a tree diagram to determine the sample space and find the probabilities for the selections of the two bands in the finals. Express probabilities as simplified fractions. Part: 0/6 Part 1 of 6 (a) The sample space contains outcomes.

The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 2. A. What precent of students consume betweem 8 and 12 pizzas per month? B. What precent of student consume MORE than 12 pizzas per (include percent signs in your answers) month?

A jar contains 4 red marbles numbered 1 to 4 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability of the given event. (a) The marble is red Your answer is: (b) The marble is odd-numbered Your answer is: (c) The marble is red or odd-numbered Your answer is: (d) The marble is blue and even-numbered Your answer is:

Three marbles are drawn, one at a time and without replacement, from a bag that contains 14 marbles: 4 red marbles 4 blue marbles 6 green marbles. What is the probability that all three marbles are the same color? Enter your answer as a fraction, not a decimal approximation. You do not need to simplify the fraction. Submit Quest

A random sampling of chicken in supermarkets revealed that approximately 80% was contaminated with an organism. Of the contaminated chicken, 20% had the strain that is resistant to antibiotics. Construct a relative frequency distribution showing the following outcomes when chicken is purchased at a supermarket: U: the chicken is not infected with the organism; C: the chicken is infected with the nonresistant organism; R: the chicken is infected with the resistant organism. P(U) = P(C) P(R) = =

A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $500. If they offer a 2 year extended warranty for $49, what is the company's expected value of each warranty sold? S

Jenelle draws one from a standard deck of 52 cards. Determine the probability of drawing either a jack or a ten? Write your answer as a reduced fraction. Answer = Determine the probability of drawing either a jack or a heart? Write your answer as a reduced fraction. Answer =

Calculate the relative frequency P(E) using the given information. Eight hundred adults are polled and 320 of them support universal health-care coverage. E is the event that an adult does not support universal health coverage. HINT (See Example 1.1 MY NOTES P(E) ASK YOUR TEACHER PRACTICE ANOTHER

2. Lisa and Bart spin this spinner 60 times. The results are below: Black Blue Purple Orange Color Black Times 17 Spun Blue Orange Purple 15 21 7 a) What is the experimental probability of a spin of orange? b) Which color had an experimental probability that matched its theoretical probability?

Compute the indicated quantity. P(A n B) = P(A) = 0.1, P(B) = 0.3. A and B are independent. Find P(An B).

Compute the indicated quantity. P(A n B) = P(A) = 0.8, P(B) = 0.2. A and B are independent. Find P(A n B).

Determine if the events Q and R are independent based on the following information. Round to two decimal places if necessary. P(Q) = 0.67 P(R) = 0.22 P(Q∩R) = 0.15 Not enough information to determine independence. Yes, the events are independent. No, the events are not independent.

Currently Samsung ships 23.2 percent of the organic light-emitting diode (OLED) displays in the world. Let S be the event that a randomly selected OLED display was made by Samsung. (a) Find P(S). (Round your answer to 3 decimal places.) (b) Find P(S). (Round your answer to 3 decimal places.)

Determine whether the following experiment satisfy the conditions for a binomial probability experiment. A ball is drawn from a bag containing 5 white and 8 red balls and then replaced. This is done a total of 5 times, and the number of times a red ball is drawn is recorded. Maybe No Impossible Cannot be determined Yes

According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual.

Sandra bought a Mega Millions ticket for $10. 100 million tickets have been sold for the game. One ticket is drawn for a $10 million prize money. What is the expected value of a ticket? O-$0.099 O-$0.99 O-$9.9 O-$99 What will be the implication if Sandra bought 1000 tickets? Sandra will lose oby $9900 X

Do one of the following, as appropriate: (a) Find the critical value Za/2, (b) find the critical value to/2. (c) state that neither the normal nor the t distribution applies. 91%; n = 45; σ is known; population appears to be very skewed. Za/2= 1.75 Za/2= 1.70 ta/2 = 1.34 ta/2= 1.645

A company estimates that 0.6% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $300. If they offer a 2 year extended warranty for $23, what is the company's expected value of each warranty sold?