Question

1. An analyst for the superintendent’s office decides to examine the attendance of 500 randomly selected students by their grade. Her data is shown in the table below:

Days Absent	Grade Level
	E5 K to 6th	E6 7th to 9th	E7 10th & Above	Total
E1 >=10 days	e1 10	e2 15	e3 25	50
E2 3 to 9 days	e4 65	e5 55	e6 80	200
E3 1 to 2 days	e7 75	e8 50	e9 25	150
E4 0 days	e10 35	e11 45	e12 20	100
Total	185	165	150	500

1. Compute the frequencies of each event and elementary event.
2. What is the probability of either event E₁ or E₄, or both occurring?
3. What is the probability of both events E₃ and E₇ occurring? Which elementary event(s) represents both events E₃ and E₇ occurring?
4. What is the probability of either event E₃ or E₇ occurring?
5. What is the probability a student will miss 1 to 2 days, given the student is in the K-6^th grade level?
6. What is the probability a student will miss more than two days, given the student is in grade 10 or above?

Answer 1

a)

Days Absent	Grade Level
	E5 K to 6th	E6 7th to 9th	E7 10th & Above	Total
E1 >=10 days	e1 10	e2 15	e3 25	50
E2 3 to 9 days	e4 65	e5 55	e6 80	200
E3 1 to 2 days	e7 75	e8 50	e9 25	150
E4 0 days	e10 35	e11 45	e12 20	100
Total	185	165	150	500

The value given in the above table are frequencies of each Event and elementary event

b)

Probability (P) = Favourable Outcome (F) / Total Outcome (T)

Total Outcome = ⁵⁰⁰C₁ = 500

E1 or E4 or both. Since both E1 and E4 cannot occur simultaneously

Favourable Outcome (F) = ⁵⁰C₁ + ¹⁰⁰C₁ =150

Hence P = 150/500 = 0.3

c)

E3 and E7 both occurring simultaneously

F = ²⁵C₁ =25

P = 25/500 = 0.05 or 5%

Elementary event e9 represents both events E₃ and E₇ occurring

d)

either event E₃ or E₇

F = ¹⁵⁰C₁ + ¹⁵⁰C₁ - ²⁵C₁ =275

P = 275/500 = 0.55 or 55%

e)

probability a student will miss 1 to 2 days, given the student is in the K-6^th grade level

F = ⁷⁵C₁ =75

P = 75/500 = 0.15 or 15%

f)

probability a student will miss more than two days, given the student is in grade 10 or above?

F = ⁸⁰C₁ +²⁵C₁=105

P = 105/500 = 0.21 or 21%