Bayes’ rule can be used to identify and filter spam emails and text messages. A large collection of real SMS text messagesfrom participating cellphone used in this research. In this collection, 747 of the 5574 total messages (13.40%) are identified as spam.

2.The word “free” is contained in 4.75% of all messages, and 3.57% of all messages both contain the word “free” and are marked as spam.a)What is the probability that a message contains the word “free”, given that it is spam?b)What is the probability that a message is spam, given that it contains the word “free”?

### Want to see the full answer?

Check out a sample Q&A here*star_border*

## Related Statistics Q&A

Find answers to questions asked by students like you.

Q: 1. A committee of eight people must choose a president, a vice president and a secretary. In how man...

A: Number of ways three positions can be chosen:When there are n items, the number of ways x items can ...

Q: Describe the main difference between a dependent and an independent t test. (Note: I am not asking y...

A: Dependent t-test: The dependent t-test, also known as the “paired t-test”, is a statistical procedur...

Q: 9.3 Question is in the attached picture.

A: a. Identifying whether the linear combination are contrast:Contrast:A contrast is linear combination...

Q: You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, ...

A: According to the given question, x be the age of the calf (in weeks), and let y be the weight of the...

Q: How many ways can a dinner patron select 3 appetizers and 2 vegetables if there are 6 appetizers and...

A: Total number of available appetizers = 6Number of appetizers to be selected = 3Total number of avail...

Q: In a normal distribution of pain estimates (0 = no pain, 100 = lots of pain) where μ = 25 and σ = 11...

A: The given information is that the normal distribution of pain estimates with mean 25 and standard de...

Q: Number 15 A B C D

A: Note:Thank you for the question. However, your question has more than 3 parts. We are solving first ...

Q: Members of the school committee for a large city claim that the population mean class size of a midd...

A: According to the question,H0: μ=20 versus Ha: μ<20We have n = 35Level of significance = 0.05t = -...

Q: A genetic experiment involving peas yielded one sample of offspring consisting of 430 green peas and...

A: State the appropriate hypothesis:Let p be the population proportion of yellow offspring peas.The giv...

*question_answer*

Q: 10) Two cards are drawn from a standard deck of 52 cards and the first is not replaced before the se...

A: In this question, we have to draw two cards from a deck of 52 cards without replacement. Then we hav...

*question_answer*

Q: How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and r...

A: In this question, we have the weighs of adult wild mountain lions, which is681071251276064 Using tha...

*question_answer*

Q: For mode of Beta Distribution with parameters Alpha and Beta, why are the bounds when alpha and beta...

A: Beta FunctionIt is an area function and defined by a definite integral

*question_answer*

Q: 3.) A card is selected from an ordinary deck of 52 cards. What is the probability of getting (Exampl...

A: a)Face cards are of jack, queen and king in each suit.Therefore in the suit of clubs there will be t...

*question_answer*

Q: The following is data for the first and second Quiz scores for 8 students in a class. First Quiz ...

A: (1)The given data about the first and second quiz scores of 8 students.Software procedure:Step by st...

*question_answer*

Q: How do you determine the mean annual return?

A: The mean of any given data is nothing but the average of the data.Let X1, X2 , X ,....., Xn are n da...

*question_answer*

Q: In a study of minimizing tractor skidding distances along a new road in a European forest, the skidd...

A: Here, the sample size (n) is 20.The mean and standard deviation of the sample data is calculated bel...

*question_answer*

Q: A student takes a multiple choice test that has 11 questions. Each question has four choices. The st...

A: Identifying the distribution:It is given that the student takes a multiple choice test that has 11 q...

*question_answer*

Q: A hospital reported that the normal death rate for patients with extensive burns (more than 40% of s...

A: (a) Level of significance:It is given that to test the claim that the mortality rate has dropped, l...

*question_answer*

Q: We use the form ŷ = a + bx for the least-squares line. In some computer printouts, the least-squar...

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,...

*question_answer*

Q: You draw and keep a single coin from a bowl that contains 12 pennies, 9 dimes, and 20 quarters. What...

A: The given information is that the bowl contains the12 pennies, 9 dimes, and 20 quarters.It is known ...

*question_answer*

Q: Fuming because you are stuck in traffic? Roadway congestion is a costly item, both in time wasted an...

A: Hey, since there are multiple subpart questions posted, we will answer first three subparts. If you ...

*question_answer*

Q: Over the past several months, an adult patient has been treated for tetany (severe muscle spasms). T...

A: Confidence interval when population standard deviation is not known:The formula of confidence interv...

*question_answer*

Q: How much money do winners go home with from the television quiz show Jeopardy? To determine an answe...

A: Solution:Confidence interval formula:Confidence interval = sample statistic ± margin of errorWhere, ...

*question_answer*

Q: A sample of 50 women is obtained, and their heights (in inches) and pulse rates (in beats per mi...

A: According to the provided data, the variable x represents the height of the women. The sample size, ...

*question_answer*

Q: The state superintendent of schools consistently states that the average salary of all substitute te...

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you. ...

*question_answer*

Q: In a study of 420,077 cell phone users, 107 subjects developed cancer of the brain or nervous system...

A: Given hypothesis test let p be the proportion of cellphone users develop cancer or brain or nervous ...

*question_answer*

Q: If a chicken and a half lays an egg and a half in a day and a half how many eggs can 30 chickens lay...

A: It is given that a chicken and a half lays an egg and a half, in a day and half.That is, 1.5 chicken...

*question_answer*

Q: What degrees of freedom would younormally expect a t test to have when N1 = 40 and N2 = 55?

A: It is provided that there are two samples of size n1=40 and n2=55.So, this is an example of 'two sam...

*question_answer*

Q: yai ayu, au uiaı uie iwu aapico aI IIupcInuc J pi IaIuvII apico ocicLICu 1VIITIVILIany uiouIvulcu pu...

A: Solution:Null and alternative hypotheses:The null and alternative hypotheses to test is given below:...

*question_answer*

Q: (a) In the random number table, assign the digits 0 through 8 to the event "successful surgery" and ...

A: Total number of digits assigned to event "successful surgery" (0-8) = 9Total number of digits assign...

*question_answer*

Q: Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took th...

A: Given data of glucose reading for 8 weeks92 87 82 107 99 109 85 89The sample x-bar is 93.8 . x is no...

*question_answer*

Q: Let z=a be a positive z-score in a standard normal distribution such that the area between z=-a and ...

A: Normal distribution:A random variable X is said to follow a normal distribution if the probability d...

*question_answer*

Q: For what types of data would you use nonparametric verses parametric statistic?

A: In hypothesis testing, the parametric tests are used to make inference on some unknown parameters ba...

*question_answer*

Q: Listed below are the number of cricket chirps in 1 min and the corresponding temperatures in degrees...

A: In this question we have given the data about no. of chirps in 1 min and the corresponding temperatu...

*question_answer*

Q: The same media consultants decided to continue their investigation of the focal relationship between...

A: Regression analysis:Regression analysis estimates the relationship among variables. That is, it esti...

*question_answer*

Q: Statistics Question

A: According to the provided information, the variable ‘x’ be age of the best actress winner and ‘y’ be...

*question_answer*

Q: See the attached question.

A: Introduction to binomial distribution:Consider a random experiment involving n independent trials, s...

*question_answer*

Q: Describe when a given distribution is a probability distribution.

A: Let us assume X be a random variable such that X connected with the outcome of a random experiment w...

*question_answer*

Q: What is a CI and what information is required to set up a CI?

A: CI:CI represents confidence interval.

*question_answer*

Q: See attachment for question.

A: Introduction to binomial distribution:Consider a random experiment involving n independent trials, s...

*question_answer*

Q: Five children aged 2, 3, 5, 7 and 8 years old weigh 14, 20, 32, 42 and 44 kilograms respectively. Fi...

A: Let x be the age of children and y be the weight of children.The equation of the regression line is:

*question_answer*

Q: Workers at a large toxic cleanup project are concerned that their white blood cell counts may have b...

A: Let the random variable X be the white blood cell count per cubic millimetre of whole blood in a hea...

*question_answer*

Q: Leah Peschel is the bottling department manager for a bottling company that produces various soft dr...

A: GivenNull hypothesis H0: µ1 = µ2Alternative hypothesis Ha : µ1 ≠ µ2Sample mean number of cola bott...

*question_answer*

Q: A manufacturer of a certain type of hardware has two manufacturing facilities and wants to compare t...

A: Conditions:The conditions for the two proportion test for sample sizes n1 and n2 with sample proport...

*question_answer*

Q: what would be the mean and standard deviation of each chart!! I am having trouble calculating this. ...

A: Calculation: Mean:Before mean:Control: (5 + 1 + 2)/3 = 2.67. [(Before Stephanie + Before Brenda + Be...

*question_answer*

Q: For frecuency distribution for us governor 2019. Party. Frequency Democratic. ...

A: Given question have more than three sub parts. According to our policies cannot answer more than thr...

*question_answer*

Q: What is the condition on the probability of success p that will guarantee the histogram of a binomia...

A: The binomial distribution has p - probability of success and n- number of trails. The binomial distr...

*question_answer*

Q: Recall that Benford's Law claims that numbers chosen from very large data files tend to have "1" as ...

A: Hello there! there are moe than three subparts in the question. According to our policies cannot ans...

*question_answer*

Q: Listed below are the amounts of mercury (in parts per million, or ppm) found in tuna sushi sample...

A: In this question, we have the data of amount of mercury in tuna sushi stores using the data we have ...

*question_answer*

Q: The book states the following: "The smaller our sample size and the more extreme the outlier score i...

A: We know from equation 1 below that the width of confidence interval is inversely proportional to the...