Question

The following contingency table refers to marriage and education. Marriage M M' Total D 1000 2000 3000 Education D' 500 1500 2000 Total 1500 3500 5000 M = Married M1 = single (not married) D = person has degree D1 = person doesn’t have a degree. 1. Compute all the marginal and joint probabilities.

Answer 1

Contingency table

Married (M) Not married (M1) Total

Degree(D) 1000 2000 3000

No Degree (D1) 500 1500 2000

Total 1500 3500 5000

Marginal Probabilities

P(D) = (Number of person having degree)/(Total number of persons) = 3000/5000 = 3/5 = 0.60

P(D1) = (Number of persons without degree)/(Total number of persons) = 2000/5000 = 2/5 = 0.40

P(M) = (Number of married persons )/(Total number of persons) = 1500/5000 = 3/10 = 0.30

P(M1) = (Number of unmarried persons )/(Total number of persons) = 3500/5000 = 3/10 = 0.70

Joint Probabilities

P(DM) = (Number of married persons with degree)/(Total number of persons) = 1000/5000 = 1/5 = 0.20

P(DM1) = (Number of unmarried persons with degree)/(Total number of persons) = 2000/5000 = 2/5 = 0.40

P(D1M) = (Number of married persons without degree)/(Total number of persons) = 500/5000 = 1/10 = 0.10

P(D1M1) = (Number of unmarried persons without degree)/(Total number of persons) = 1500/5000 = 3/10 = 0.30

Probability distribution

Married (M) Not married (M1) Total

Degree(D) 0.20 0.40 0.60

No Degree (D1) 0.10 0.30 0.40

Total 0.30 0.70 1.00