In a large introductory statistics lecture​ hall, the professor reports that 5656​% of the students enrolled have never taken a calculus​ course, 2525​% have taken only one semester of​ calculus, and the rest have taken two or more semesters of calculus. The professor randomly assigns students to groups of three to work on a project for the course. You are assigned to be part of a group. What is the probability that of your other two​ groupmates, ​a) neither has studied​ calculus?  Provide the probability that neither of your other two groupmates has studied calculus  ​b) both have studied at least one semester of​ calculus? ​c) at least one has had more than one semester of​ calculus?   Please show the work.  This question came off the homework online.

Q: n a recent survey of 619 Salinas residents, 437 stated they experienced significant traffic delays…

A: 437 stated they experienced delay 182 not experienced delay 619 total

Q: In a survey of consumers aged 12 and​ older, respondents were asked how many cell phones were in use…

A: In a survey of consumers aged 12 and​ older, respondents were asked how many cell phones were in use…

Q: In 2014, approximately 13% of nonelderly Americans adults had no health insurance. Suppose that a…

A: Given: Proportion of American adults having no health insurance, p=0.13 Sample size, n=400

Q: A survey of athletes at a high school is conducted, and the following facts are discovered: 38% of…

A: P( athletes playing football) = P(F) = 0.38 P( athletes playing basketball) = P(B) = 0.28 P(…

Q: A study contains 31 women and 24 men. If 3 subjects are randomly selected without replacement, what…

A: Solution-: We have, Number of women =31, Number of men =24            Total number of persons (Women…

Q: From the research conducted by a Cancer Research Institute, it has been found that 5 percent of male…

A: Number of male cancer patients = 50 Number of female cancer patients = 50 Total number of cancer…

Q: In a study of blood donors, 125 were classified as group O and 195 had a classification other than…

A: The objective of this question is to find the probability that a blood donor will have group O…

Q: The conditional algebritis affects 15% of college professors. The blood test for algebritis…

A: From the given information, The percentage of affect is 15% That is, P(affect)=0.15 and P(not…

Q: A nationwide survey of seniors by the University of Michigan reveals that almost 30.0% disapprove of…

A:

Q: A survey of athletes at a high school is conducted, and the following facts are discovered: 26% of…

A: Given that  A survey of athletes at a high school is conducted. 26% of athletes are football…

Q: Of 500 employees at a university, 45% are female. A sample size of 60 employees is chosen at random.…

A: Note: Use the finite correction factor if n/N is greater than 0.05. Therefore, the Finite…

Q: On average, 5.5 shoplifting incidents occur per week at an electronics store.  What is the…

A: Poisson Distribution :  A Poisson distribution is a discrete probability distribution that applies…

Q: 16 of the 200 digital video recorders​ (DVRs) in an inventory are known to be defective. What is the…

A: Given that, 16 of the 200 digital video recorders​  (DVRs) in an inventory are known to be…

Q: If 10% of men are bald, what is the probability that fewer than 100 in a random sample of 900 are…

A: Solution:Binomial distribution approximated to normal distribution or not is checked below:It is…

Q: In a study of 44 patients at a rural hospital, there were 9 females in the ICU, 6 females in the…

A:

Q: Of the cartons produced by a​ company, 10​% have a​ puncture, 8​% have a smashed​ corner, and 1.3​%…

A:

Q: If 25 percent of students at a particular school use mechanical pencils, what is the probability of…

A:

Q: In a survey of consumers aged 12 and​ older, respondents were asked how many cell phones were in use…

A: Given: Number of respondents answered none = 208 Number of respondents answered one = 295 Number of…

Q: In a poll conducted on February 3 through 18 in 2021  41% of the United States was found to be…

A: According to the given information,Probability of success, p = 41% = 0.41Sample size, n = 10Let X be…

Q: subjects who have received and not received a speeding ticket in the last year, and the color of…

A: From the available information , the table is,   Red car Not red car Total Speeding ticket 45…

Q: A study of 180 randomly selected American Airlines flights showed that 68 arrived late. What is the…

A: No. of American flights =180 No. of american flights arrived late=68

Q: Of the cartons produced by a​ company, 4​% have a​ puncture, 7​% have a smashed​ corner, and…

A: Given that, 4% have a puncture 7% have a smashed corner 1.3% have both a puncture and a smashed…

Q: Atlantic Airways flights were late (arrived or departed 15 minutes late or more). A random sample of…

A: We have given that  Number of trials n=140 Success of probability p =20.4%=0.204 We use normal…

Q: In a survey of consumers aged 12 and​ older, respondents were asked how many cell phones were in use…

A:

Q: In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use…

A: From the given information ,Total respondents = 201 + 296 + 376 + 138 + 117 .…

Q: Suppose the prevalence of type II diabetes in a community is 36%. Researchers want to sample 16…

A: Suppose the prevalence of type II diabetes in a community is 36%. Researchers want to sample 16…

Q: In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use…

A:

Q: 28 of the 100 digital video recorder in an inventory are known to be defective. What is the…

A: Given: The number of defective digital video recorders is 28. The total number of digital video…

Q: A survey of California community college statistics students were asked their student status and…

A: Solution

Q: According to TMUSS Quarterly (Totally Made-Up Sports Statistics) April 2017, the probability that…

A: Let us denote: Tampa Bay Buccaneers will score a touchdown on their opening drive = A  the defense…

Q: university study involves a simple random sample of 26 students taken from a population of​ 12,550.…

A: Given that Simple random sample size (n) = 26 Population size  = 12,550 Undergraduate students make…

Q: In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use…

A: Obtain the probability that his/her household has four or more cell phones in use. The probability…

Q: Eleven of the 50 digital video recorders (DVRs) in an inventory are known to be defective. What is…

A: The number of defective video recorders is 11.

Q: Of the cartons produced by a​ company, 7​% have a​ puncture, 10​% have a smashed​ corner, and 1.1​%…

A:

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.