Question 1

a. The following two-way contingency table gives the breakdown of the population in a particular locale according to age and number of vehicular moving violations in the past three years;

Age	Violations
0	1	2+
Under 21	0.04	0.06	0.02
20 - 40	0.25	0.16	0.01
41 - 60	0.23	0.10	0.02
60+	0.08	0.03	0.00

A person is selected at random. Find the following probabilities. i. A person is over 30 years.

ii. The person has had at least two violations in the past three years. iii. The person has had at least two violations in the past three years, given that he is under 21. iv. The person is under 21, given that he has had at least two violations in the past three years. v. Determine whether the events, "the person is under 21" and "the person has had at least two violations in the past three years" are independent or not

Question 2

b. A breakdown of students enrolled in a University course by class (F: freshman, So: sophomore, J: liberal arts, O: other) academic major (S: science, mathematics, or engineering, L: liberal arts, O: other) is shown in the two-way classification table.

Major	Class
F	So	J	Se
S	92	42	20	13
L	368	167	80	53
O	460	209	100	67

A student enrolled in the course at random. Find the probability of each of the following events.

i. The student is a freshman. ii. The student is liberal arts major. iii. The student is freshman liberal arts major. iv The student is either a freshman or liberal arts major.

v. The student is not a liberal arts major.