ID	School Enrolled	Months Enrolled	Birthday Month	Distance to Work (whole miles)	Height (whole inches)	Foot Size (whole inches)	Hand Size (whole inches)	Sleep (minutes)	Homework (minutes)
1	Arts and Sciences	12	January	0	60	8	5	360	30
2	Applied Science and Technology	6	February	0	62	7	6	400	45
3	Business and Management	8	April	5	66	10	7	420	60
4	Nursing	10	June	10	68	12	8	440	15
5	Public Service	48	July	15	68	14	8	540	75
6	Arts and Sciences	48	June	30	70	12	9	480	120
7	Applied Science and Technology	36	October	32	72	11	8	320	80
8	Applied Science and Technology	32	November	36	75	14	7	440	60
9	Applied Science and Technology	10	September	14	71	12	8	330	60
10	Arts and Science	36	December	10	67	7	8	240	120
11	Applied Science and Technology	7	August	8	75	12	8	300	60
12	Applied Science and Technology	49	November	15	68	10	7	390	60
13	Applied Science and Technology	27	July	1	68	11	7	390	180
14	Applied Science and Technology	26	January	18	72	12	8	450	60
15	Applied Science and Technology	12	November	5	72	11	8	390	30
16	Applied Science and Technology	36	July	31	73	12	9	420	60
17	Arts and Science	6	April	2	63	7	5	420	60
18	Applied Science and Technology	10	October	32	72	11	8	390	45
19	Arts and Science	3	June	6	64	9	6	360	120
20	Business and Management	12	August	12	72	10	8	360	120
21	Applied Science and Technology	12	March	45	66	7	5	320	60
22	Applied Science and Technology	12	February	5	74	12	8	360	60
23	Arts and Sciences	49	March	5	65	9	7	420	120
24	Applied Science and Technology	18	September	15	72	12	7	420	90
25	Applied Science and Technology	1	March	25	70	12	7	360	90
26	Applied Science and Technology	1	August	5	68	10	7	420	90
27	Arts and Sciences	4	April	0	65	7	6	420	120

Using the results in the Student Data Table, determine the following probabilities based on the variables Birthday Month and School Enrolled.

1. Probability of a student having a June birthday.
2. Contingency table of having a June birthday by students in Applied Science and Technology or not.
   1. Show the probability of a student having a birthday in June on the contingency table.
   2. P(June birthday AND Not in Applied Science and Technology)
   3. P(June birthday OR Not in Applied Science and Technology)
   4. P(June birthday GIVEN Not in Applied Science and Technology)
3. Drawa tree diagram that represents selecting two students, at random and without replacement, that have a June birthday.
4. Draw a tree diagram that represents selecting two students, at random and with replacement, with a June birthday.
5. Explain why 3 and 4 have different outcomes.