Question

The educational level and employment status for a number of adults in a city is summarized on the accompanying table. One person is to be selected at random.

	No Hight School	High School	Some Post-secondary Education	Post-secondary Degree	Total
Employed	20	85	65	110	280
Unemployed	18	31	17	9	75
Total	38	116	82	119	355

a) What is the probability the selected person has a post-secondary degree or is employed? [1]

b) Are the events “selecting a person with a post-secondary degree” and “selecting an employed person” disjoint (mutually exclusive)? [2]

c) What is the probability of selecting a person with no high school education? [1]

d) Are the events “No high school education” and “Unemployed” independent? [2]

Answer 1

a) The probability that the selected person has a post-secondary degree or is employed

= [ n(employed) + n(post-secondary degree) - n(employed and post-secondary degree) ] / n(Total)

= (280 + 119 - 110) / 355

= 0.8141

Therefore 0.8141 is the required probability here.

b) As we know here that:
n(employed and post-secondary degree) = 110 > 0, therefore the two events are not disjoint events here.

c) P(no high school education)

= 38 / 355

= 0.1070
Therefore 0.1070 is the required probability here.

d) P(unemployed) = 75 / 355 = 0.2113
P(no high school education) = 0.1070

P( unemployed and no high school education) = 18/355 = 0.0507

P(unemployed)P(no high school education) = 0.2113*0.1070 = 0.0226 which is not equal to P( unemployed and no high school education) .

Therefore the two events are not independent here.