Mathematics, statistics 150

Question

 Employment data at a large company reveal that 53 % of the 

workers are married, that 45 % are college graduates, and 

that 1/6 of the college graduates are married. 

What is the probability that a randomly chosen worker is: 

a) neither married nor a college graduate? 

Answer =  % 

b) married but not a college graduate? 

Answer =  % 

c) married or a college graduate? 

Answer =  %

Answer 1

P(Married) = 0.53

P(College Graduate) = 0.45

a) P(Neither Married nor College Graduate) = 1 - [P(Married ∪ College Graduate)]

= 1 - (0.53 + 0.45 - 0.2385)

= 1 - 0.7415 = 0.2585

b) P(Married and Not College Graduate) = P(Married)*P(Not College Graduate)

= (0.53)*(0.55)

= 0.2915

c) P(Married or College Graduate) = P(Married) + P(College Graduate) - P(Married and College Graduate)

= 0.53 + 0.45 - 0.2385 = 0.7415

Answer 2

Event A = Married

P(A) = 0.53

Event B = Grad

P(B) = 0.45

P(A and B) = 1/6 = 0.167

a) neither married or college student

= 1 - probability married or a college student

= 1 - (P(A) + P(B) - P(A and B))

= 1 - (0.53 + 0.45 - 0.167) = 0.187 = 18.7%

b) married but not a college graduate

P(A) = P(A and B) + P(A and not B) (law of total probability)

P(A and not B) = P(A) - P(A and B)

P(A and not B) = 0.53 - 0.167 = 0.363 = 36.3%

c) married or a college graduate

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.53 + 0.45 - 0.167 = 0.823 = 82.3 %