Question

Students at Praline High are allowed to sign up for one English class each year. The numbers of students signing up for various English classes for the next school year are given in the following table: Grade English I English II English III English IV Total 10th 60 165 20 15 260 11th 35 40 115 10 200 12th 10 25 90 145 270 Total 105 230 225 170 730

Part A: What is the probability that a student will take English IV? (2 points)

Part B: What is the probability that an 11th-grader will take either English II or English III? (2 points)

Part C: What is the probability that a student will take English III given that he or she is in the 11th grade? (2 points)

Part D: Consider the events "A student takes English I" and "A student is a 10th-grader." Are these events independent? Justify your answer. (4 points)

Answer 1

	English I	English II	English III	English IV	total
10th	60	165	20	15	260
11th	35	40	115	10	200
12th	10	25	90	145	270
total	105	230	225	170	730

A)

probability that a student will take English IV =170/730=0.2329

B)

probability that an 11th-grader will take either English II or English III =(40+115)/730 =0.2123

c) probability that a student will take English III given that he or she is in the 11th grade

=115/200 =0.575

D)

since P(A) =105/730 =0.1438

P(B) =260/730=0.3562

P(A n B) =60/730 =0.0822

P(A)*P(B) =0.1438*0.3562=0.0512

since P(A)*P(B) is not equal to P(A n B) ; A and B are not independent