An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 106 students in the school. There are 39 in the Spanish class, 35 in the French class, and 24 in the German class. There are 12 students that in both Spanish and French, 4 are in both Spanish and German, and 7 are in both French and German. In addition, there are 2 students taking all 3 classes. a)If one student is chosen randomly, what is the probability that he or she is taking at least one language class? b)If two students are chosen randomly, what is the probability that neither of them is taking Spanish?

Question

 An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 106 students in the school. There are 39 in the Spanish class, 35 in the French class, and 24 in the German class. There are 12 students that in both Spanish and French, 4 are in both Spanish and German, and 7 are in both French and German. In addition, there are 2 students taking all 3 classes.

a)If one student is chosen randomly, what is the probability that he or she is taking at least one language class?

b)If two students are chosen randomly, what is the probability that neither of them is taking Spanish?

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Probability

Basic Probability

Related Probability Q&A

Find answers to questions asked by students like you.

Q: In Lixue’s garden, the green pepper plants grew 5 inches in 3/4 month. At this rate, how many feet c...

A: The green pepper plants grew 5 inches in 3/4 month 5 inches =5/12 foot

Q: Suppose you take independent random samples from populations with means μ1 and μ2 and standard devia...

A: GIVEN: Two independent random samples from populations with  means-μ1 and μ2 standard deviations -σ1...

Q: To make orange fizz Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoops of powd...

A: Given : To make orange fizz, Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoop...

Q: Use the given data to find the minimum sample size required to estimate a population proportion or p...

A: Click to see the answer

Q: 5.5

A: Let X be a random variable then the formula of hyper geometric distribution is; P(X=k)=KkN-Kn-kNn wh...

Q: 4.3-10

A: The given information: fx=110, x=0, 1, 2, .......9hy|x=110-x, y=x, x+1, x+2.....9

Q: Consider a political discussion group consisting of 5 ​Democrats, 5 ​Republicans, and 5 Independents...

A:   A political discussion group consisting 15 members out of which 5 are Democrats, 5 are Republicans...

Q: Let C be a unit circle centered at origin. Point P1 is chosen randomly from the circumference of C. ...

A: Here ,let the first point(P1) on the circumference of the circle be depicted as  (x0,y0) and the sec...

Q: Construct a Venn diagram representing each event. a.​ (​F & (not M)) b.​ ((F or M) ​& (not ​...

A: Click to see the answer

Q: One card is drawn from a well-shuffled deck of 52 cards. Find the following.   a) Probability of get...

A: Introduction: The probability of an event in an experiment is the number outcomes in the experiment ...

Q: Mark each statement TRUE or FALSE. For these problems, assume that to estimate average time spent wa...

A: It is given that the sample size is 10.

Q: In China, 4-year-olds average 3 hours a day unsupervised. Most of the unsupervised children live in ...

A: Let us denote X=number of hours unsupervised. Given that X follows a normal distribution with mean=3...

Q: The average full-sized front-loading Energy Star clothes washer uses 15 gallons of water per load (g...

A: The average full-sized front-loading Energy Star clothes washer uses 15 gallons of water per load. A...

Q: Suppose the table summarizes the opinions of various groups on the issue of oil drilling in national...

A: Given that there are total (20+15+30+185)=250 non-whites Among them (30+185)=215 opposes oil drillin...

Q: In the transmission of digital information, the probabilities that a bit has high, moderate and low ...

A: Given that  P(high)=0.01 P(moderate)=0.04 P(low)=0.95 n=5 and the amount of distortion of each bit i...

Q: An ACME Bearings manager wants to compare the average ball bearing sizes from two different machines...

A: a)  Necessary assumptions for constructing the t-interval are: i) The sample standard deviation are ...

Q: The weight of a sophisticated running shoe is normally distributed with a mean of 12 ouncesand a sta...

A: A z-score represents the position of a data point in terms of its distance from the mean when measur...

Q: A sample space contains six sample points and events AA, BB, and CC as shown in the Venn diagram. Th...

A: From the venn diagram, event A consists of the sample points 1, 2, 3.    So, the  probability of A w...

Q: Suppose that in a particular Finite course, 5/14 of students plan on majoring in math, 11/42 plan on...

A: Given information- We have given the proportion of particular Finite course. P (Major in math) = 5/1...

Q: In the transmission of digital information, the probabilities that a bit has high, moderate and low ...

A: Given that, the probability that a bit has high distortion is 0.01. Therefore, P(A)=0.01 The probabi...

Q: 2]. Let the events A = {x 0.75}. (a) Find the probabilities of A, B, A N B, and A Nc. (b) Find the ...

A: Calculate the events of A,B and C. A=[-1,0) Since, A=x<0. Given that, B=|x-0.5|<0.5 Thus, x-0....

Q: Rework problem 8 from section 3.1 of your text, involving events E, F, and G in a sample space S. As...

A: 1) It is given that, Pr[E]=0.55, Pr[F]=0.35,  Pr[G]=0.35, Pr[E∩F]=0.25, Pr[E∩G]=0.25, Pr[F∩G]=0.15, ...

Q: A line passes through the points (9, 8) and (0, 7). What is its equation in slope-intercept form? Wr...

A: Given points (9,8) and (0,7)

Q: Workings needed also, thank you.

A: Note- As per our policy we can answer only the first 3 sub-parts of a question. If you want solution...

Q: 2. IOP create billions of dollars of new wealth for owners, managers, and employees of companies tha...

A: As per honor code, we will only answer first three part of the question. a)  The population in this ...

Q: A normal population has a standard deviation of 10. A random sample of 100 is taken to test H0:μ = 5...

A: Given: H0:μ = 50 H1:μ ≠ 50

Q: Find the indicated probability assuming that x is a random variable with a normal distribution with ...

A: It is given that the mean is 100 and standard deviation is 25.

Q: A work crew for a building project is to be made up of 2 craftsmen and 4 laborers selected from a to...

A: a) Let us consider there is one building project. The possible combinations to select 2 out of total...

Q: Workings needed please

A: Hey there! Thank you for posting the question. Since there are multiple questions posted, we will an...

Q: How to write the statement "n^2 is odd whenever n is odd" in logical form.

A: The given statement is "n2 is odd whenever n is odd". If the remainder is not equal to 0, when n is ...

Q: 11. Suppose X and Y are independent continuous random variables uniformly dis- tributed on the inter...

A: Given information X and Y independent continuous random variables follows uniform distribution  0 ≤ ...

Q: Suppose that the annual rainfall in Ferndale, California, is known to be normally distributed, with ...

A: Let "X" be the annual rainfall in Ferndale, California.  

Q: The Dynamax Company is going to introduce one of three new products: a widget, a hummer, or a nimnot...

A: a) The market condition that will estimate the profit and loss of the company D is given. Expected v...

Q: The records of 100 postal employees who volunteered for a study, showed that the average time these ...

A: Click to see the answer

Q: Rework problem 7 from section 3.1 of your text, involving events E, F, and G in a sample space S. As...

A: Given that: Pr[E]=0.45 , Pr[F]=0.6 , Pr[G]=0.5 , Pr[E∪F]=0.8 , Pr[E∪G]=0.7 , and Pr[F∪G]=0.8    1) W...

Q: 2. For the Cauchy distribution: 1 C(x; γ) %3D 2 (X – Xo - TY |1 + a. Derive the mean of the distribu...

A: Given the Cauchy distribution , C(x;γ)=1πγ[1+(x-x0γ)2 ] To derive mean of the distribution and the c...

Q: 11 Assume that the critic finds that 30 percent of the movies have positive comments about the plot,...

A: Let us denote: A= positive comments about the plot B=positive comments about the acting   Given that...

Q: 3) Answer part B. See pictures

A: Construct a Scatterplot for the given data: The data represents the values of points/game and yards/...

Q: Solve problem 2

A: The orders from n=100 customers for wooden panels of various thickness (X) are summarized as:   ...

Q: The soccer league in 1 community has 5 teams. You are required to predict, in order, the top 3 teams...

A: Given:  A community in Soccer league has 5 teams. The objective is to find the probability of predic...

Q: 1). prove that the waiting time for a Poisson distribution is Exponentially distributed and an Expon...

A: Click to see the answer

Q: Suppose 4-year-olds in a certain country average 3 hours a day unsupervised and that most of the uns...

A: As per honor code we will provide solutions for first three parts only. Given information: Mean = 3....

Q: Suppose a randomly selected passenger is about to go through the metal detector at FuaʻamotuInternat...

A: a) A random passenger is selected to go through the metal detector The possibility of passenger sett...

Q: A class consists of 10 male and 30 female students. Of the 30 females, only 5 did not have pet. Six ...

A: The probability of an event E  is defined as the ratio of favourable number of outcomes to the total...

Q: A trimotor plane has three engines—a central engine and an engine on each wing. The plane will crash...

A: Given that, A trimotor plane has three engines—a central engine and an engine on each wing. The plan...

Q: You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money ...

A: Solution: Compute the expected value for sister’s game:  Sister says to roll a six-sided die. She wi...