Question

PROBLEM 3: (15 points) Educational level and Smoking

At a large factory the employees were surveyed and classified according to their level of education and whether they smoked.

	Not HS graduate	HS graduate	College Graduate
Smoke	21	11	14
Do not smoke	3	9	20

If an employee is selected at random, find these probabilities:

1. The employee smokes, given that he or she graduated from college.
2. Given that the employee did not graduate from high school, he or she is a smoker.
3. Is there any relationship between education and the smoking habit? Explain it based on the probabilities’ values.            

Answer 1

Probabilities are calculated using classical definition. And independence is checked for two pairs.
solution - dat bio niso Let al Education & B: Smoking habit. The given table can be written as follows - Not HS graduate HS graduate College gpacatel Total (A2) 14 Smoke (B) Do not smoke (B2) 21 03018 Logan 20 46 32 0 Total T 24 I 20 80 34 1 78 a) The prob. that employee smokes given that helshe graduated from college =P[B1/A3] - PCBINA3) P(A3) borroedo i s old = 14778 al on 34) 78 14 P(B1/A3) = 0.4117 b) The prob. that employee is smoker gives that he/she did not graduate from high school - PCBL/A) = P(BINAI) P(A) - 21/78 = 2l = 0.875 24/78 24 PCBI LAN) = 0.875

c) Two events A & B are said to be independent if L PRADB) = P(A). P(B), otherwise they are depended Here we have events A, A₂, A3 & Bi, B2,1 We check their pairwise independence. Consider the following some of the probabilities - ( __POP; ОВ; ) | UPCA, DB)) = 2) 78 PLA). P(B; odor P(AI), P (B) = 24 46 = 1104 78 6084 2) PCA, NB2) = 3 P(As)- P(B2) = 24 32 = 768 78 78 78 6084 Similarly we can check for remaining pairs From the above table it is observed that P(ADB) & PCA) PCB; for af pain of life Ai & B; are not independent they are dependent. ie & Education and smoking habit are Canaa depexdent.