Question

In: Statistics and Probability

In a certain semester, 500 students enrolled in both Calculus I and Physics I. Of these...

In a certain semester, 500 students enrolled in both Calculus I and Physics I. Of these students, 82 got an A in calculus, 73 got an A in physics, and 42 got an A in both courses. Which of the following probabilities is the smallest? The probability that a randomly chosen student...

Got an A in both of the two courses

Got an A in physics but not calculus

Got an A in at least one of the two courses

Got an A in calculus but not in physics

Got less than an A in at least one of the two courses

Solutions

Expert Solution

Let X be the event that the student got an A in Calculus I

Y be the event that the student got an A in Physics I

So here

N = 500

n(X) = 82

n(Y) = 73

a) the probability that a randomly chosen student Got an A in both of the two courses

b) the probability that a randomly chosen student Got an A in physics but not calculus

c) the probability that a randomly chosen student Got an A in at least one of the two courses

d) the probability that a randomly chosen student Got an A in calculus but not physics

e) the probability that a randomly chosen student Got less than an A in at least one of the two courses

Please give thumbs up if you like the answer.


Related Solutions

The table below shows the number of male and female students enrolled in nursing at a university for a certain semester.
The table below shows the number of male and female students enrolled in nursing at a university for a certain semester. A student is selected at random. Complete parts (a) through (d). Nursing majorsNon-nursing majorsTotalMales9810161114Females60017292329Total69627453443(c) Find the probability that the student is not female or a nursing major. P(not being female or being a nursing major)=_______ Round to the nearest thousandth as needed.) (d) Are the events "being male" and "being a nursing major" mutually exclusive? Explain. A. Yes, because one can't be male and...
How are your grades? In a recent semester at a local university, 300 students enrolled in...
How are your grades? In a recent semester at a local university, 300 students enrolled in both Statistics I and Psychology I. Of these students, 83 got an A in statistics, 75 got an A in psychology, and 49 got an A in both statistics and psychology. Round the answers to four decimal places, as needed. A) Find the probability that a randomly chosen student got an A in statistics or psychology or both. B) Find the probability that a...
For students who first enrolled in two year public institutions in a recent​ semester, the proportion...
For students who first enrolled in two year public institutions in a recent​ semester, the proportion who earned a​ bachelor's degree within six years was 0.396 The president of a certain college believes that the proportion of students who enroll in her institution have a lower completion rate. ​(a) Determine the null and alternative hypotheses. ​(b) Explain what it would mean to make a Type I error. ​(c) Explain what it would mean to make a Type II error. ​(a)...
For students who first enrolled in two year public instituitons in a recent semester, the proportion...
For students who first enrolled in two year public instituitons in a recent semester, the proportion who earned a bachelor's degree within six years was 0.388. The president of a certain college believes that the proportion of students who enroll in her institution have a higher completion rate. A.) Determine the null & alternative hypotheses. B.) Explain what it would mean to make a Type I error. C.) Explain what it would mean to make a Type II error. A.)...
Use the student dataset for this question. students are considered “full-time” students if they are enrolled in 12 or more credits in a given semester.
Use the student dataset for this question. students are considered “full-time” students if they are enrolled in 12 or more credits in a given semester.  What percent of respondents in the student dataset are “full-time” students? Consider your result to part (a) as the best estimate for the probability of any randomly selected student being full-time. Based on that response, what is the probability that in a class of 20 students they will all be full-time?   Credits 13 12...
in a class of 25 students, 17 passed calculus, 13 passed chemistry, and 8 passed physics....
in a class of 25 students, 17 passed calculus, 13 passed chemistry, and 8 passed physics. No one passed all three, but at least six of them failed all three subjects. How many students failed all three subjects?
6. Use the table below, based on data from students enrolled in BMGT 230/230B this semester,...
6. Use the table below, based on data from students enrolled in BMGT 230/230B this semester, to answer/complete parts a. through e. (the cell values are frequencies): Sex Political Attitude Male Female Very Conservative 20 2 Somewhat Conservative 62 25 Middle-of-the-Road 100 67 Somewhat Liberal 80 62 Very Liberal 11 21 a. Determine the probability a student selected at random is Conservative (meaning either Very Conservative or Somewhat Conservative). b. Determine the probability a Male student selected at random is...
Students may choose between a 3-semester-hour physics course without labs and a 4-semester-hour course with labs.
Students may choose between a 3-semester-hour physics course without labs and a 4-semester-hour course with labs. The final written examination is the same for each section. If 12 students in the section with labs made an average grade of 84 with a standard deviation of 4, and 18 students in the section without labs made an average grade of 77 with a standard deviation of 6, find a 99% confidence interval for the difference between the average grades for the...
Students may choose between a 3-semester-hour physics course without labs and a 4-semester-hour course with labs.
Students may choose between a 3-semester-hour physics course without labs and a 4-semester-hour course with labs. The final written examination is the same for each section. If 12 students in the section with labs made an average grade of 84 with a standard deviation of 4, and 18 students in the section without labs made an average grade of 77 with a standard deviation of 6, find a 99% confidence interval for the difference between the average grades for the...
I have to do an experiment/ demonstration for my PHY251 class (Calculus based physics). I am...
I have to do an experiment/ demonstration for my PHY251 class (Calculus based physics). I am only allowed to do it on one of the following topics: Vectors, Accelerated motion, Centripetal force, Free fall, projectile motion, Inertia, Equilibrium, Friction, Orbits, Tides. Does anyone have any ideas for a cool demonstration? Please provide instructions for the demonstration/experiment. Thank you in advance.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT