Question

	Number of times	students visited	tutoring
	one or fewer times	2 or 3 times	4 or more times	total
full time students	12	25	6	45
part time students	2	5	6	13
Total	14	30	14	58

1. (a) What is the probability the student visited the tutoring center four or more times? Write your answer as a simplified fraction or a decimal to 3 decimal places. Show your work.

2. (b) What is the probability the student is full time? Write your answer as a simplified fraction or a decimal to 3 decimal places. Show your work.

3. (c) What is the probability the student visited the tutoring center four or more times, given that the student is full time? Write your answer as a simplified fraction or a decimal to 3 decimal

places. Show your work.

(d) Are number of times a student visited tutoring and the student status (full or part time) independent. Explain your answer and show all relevant work.

Answer 1

Solution(a)
P(Student visited the tutoring four pr more times) = 14/58 = 0.241
Solution(b)
P(Student is full time) = 45/58 = 0.776
Solution(c)
P(Student visited the tutoring four or more time given that student is full time) = P(Student visited the tutoring four or more time given that student is full time)/P(Full time) = (6/58)/(45/58) = 6/45 = 0.133
Solution(d)
No, the number of times a student visited tutoring and the student status is not independent because P(Student visiting tutoring and student status) is not equal to zero. So we can say that both events are not independent.