In: Statistics and Probability
DATA SET: 105, 82, 94.5, 72.5, 92, 91, 52, 86, 100, 96, 98, 109, 96, 103, 68
Data Table:
A | 10 |
B | 2 |
C | 1 |
D | 1 |
F | 1 |
Q1. Considering grade C or above as a passing grade, what is the probability for a student to receive a passing grade?
Q2. What is the probability of a student not receiving a passing grade?
Q3. What is the probability that the student received grade A or grade B?
Q4. What is the probability that the student received grade A, grade B, or grade C?
Q5. What is the probability that a student receive grade A & B?
Q6. What is the probability that a student receive grade A?
Q7. What is the probability that a student received grade B?
Q8. What is the probability that a student received grade C?
Q9. What is the probability that a student received grade D?
Q10. What is the probability that a student received grade F?
Q11. If a committee with 2 student members is to be formed, what is the probability of forming a committee with one A grade and one F grade student?
Q12. If a committee with 2 student members is to be formed, what is the probability of forming a committee with one A grade and one B grade student?
Q13. If the records whos that the probability of failing (with grade F) this course is p, [use the answer of question 11 as the probability here], what is the probability that at most 2 students out of 15 fail this course?
Q14. If the records whos that the probability of a student to get a grade B for this course is p, [use the answer to question 7 as the probability here], what is the probability that exactly 4 students out of 15 will have a grade B for the course?
Q15. What is the probability of selecting a grade A student for the first time either in 2nd or 3rd selection?
There are total 15 students.
Q1:
Out of 15 students 10+2+1 = 13 students get passing grades C, B or A so
P(passing grade) = 13 / 15
Q2:
By the complement rule, the probability that student is not receiving passing grade is
P(not passing grade) = 1 - P(passing grade) = 1 - 13/15 = 2/15
Q3:
Out of 15 students, 10+2 = 12 students received grade A or grade B so
P(grade A or B) = 12 /15 = 4/ 5
Q4:
Out of 15 students 10+2+1 = 13 students get passing grades C, B or A so
P(grade A, B or C) = 13 / 15
Q5:
No student can get both grades A and B together so
P(A and B) = 0
Q6:
P(grade A) = 10/15 = 2/3
Q7:
P(grade B) = 2/15
Q8:
P(grade C) = 1/15
Q9:
P(grade D) = 1/15
Q10:
P(grade F) = 1/15