6. (5 Marks) A group of four undergraduate and five graduate students are available to fill...
Problem #3: Let A and B be two events on the sample space S. Then show that a. P(B) P(AOB)+P(AnB) b. If Bc A, then show that P(A)2 P(B) Show that P(A| B)=1-P(A|B) C. P(A) d. If A and B are mutually exclusive events then show that P(A| AUB) = PA)+P(B) Problem 4: If A and B are independent events then show that A and B are independent. If A and B are independent then show that A and B...
Suppose that 71% of USC students graduate in four years, and 81% graduate in 6 years. If you randomly select 10 first year USC students, what is the probability that all 10 will graduate in 4 years? In 6 years?
Tradition says that an undergraduate student won’t graduate in four years if he/she walks underneath the Bell Tower at Purdue. Every time an undergraduate student walks past the tower, the probability that the student will walk underneath the tower is 0.08. Assume that each student is independent of any others. d) 6 students have walked past the bell tower and none of these students walked underneath it. What is the probability that it takes more than 14 students (total) walking...
Probabilitv: NON-Mutually Exclusive Event 4. A group of 20 students have applied to be on a university committee that will advise government on tuition fee policy. Six of the students in total are completing a Bachelor of Science degree, 12 of the students in total are completing a Bachelor of Arts degree, 2 are completing degrees in both the faculty of Arts and the faculty of Science, and 3 are completing a Bachelor of Commerce degree (Business) only. One student...
A study was conducted to determine whether there were significant differences between medical students admitted through special programs (such as retention incentive and guaranteed placement programs) and medical students admitted through the regular admissions criteria. It was found that the graduation rate was 90.4% for the medical students admitted through special programs. Be sure to enter at least 4 digits of accuracy for this problem! - If 9 of the students from the special programs are randomly selected, find the...
5. In a math class consisting of 21 students, suppose that 10 of the enrolled students are rated as “very proficient" in math, according to a standardized test. (a) (4 points) Suppose 4 students in the class are randomly selected to form a group and work on a project. What is the probability that all of the students in the group are rated as very proficient in math? (b) (4 points) If 4 students in the class are randomly selected,...
Four balls are to be randomly chosen from an urn containing 4 red, 5 green, and 6 blue balls. 1. Find the probability that at least one red ball is chosen? 2. Given that no red balls are chosen, what is the probability that there are exactly 2 green balls among the four balls chosen.
Question 2 (5 points) A group of freshmen and sophomore students was selected and each was asked whether they were a member of a student club. The following table was constructed Student No Student Club 13 11 Club Freshmarn Sophomore 10 Find the probability that a randomly selected student form the group is a freshman or is a member of a student club. Write only a number a your answer. Round to two decimal places (for example: 0.73). Do not...
6. The college health center did a campus-wide survey of students and found that 18% of the students smoke cigarettes. A group of nine students randomly come together and sit at the same table on the plaza in front of the library. Find the probability that: (a) No student at the table smokes. (b) At least one student at the table smokes. (c) More than two students smoke. (d) From one to five smoke (including one and five).