Question

Employment data at a large company revealed that 72% of the workers are married, that 48% are college graduates, and that half of the college grads are married. What is the probability that a randomly chosen worker-

a) is neither married nor a college graduate

b) is married but not a college graduate

c) is married or a college graduate

Answer 1

from above P(married )=0.72 ; P(College graduates )=0.48 ; P(married |College grads) =0.5

a)

P( neither married nor a college graduate ) =1-P(either married or college graduate )

=1-(P(married)+P(College graduate)-P(College gard)*P(married |College grads))

=1-(0.72+0.48-0.48*0.5)

=0.04

b)

P( is married but not a college graduate )=P(married)-P(College gard)*P(married |College grads))

=0.72-0.48*0.5

=0.48

c)

P( is married or a college graduate ) =P(married)+P(College graduate)-P(College gard)*P(married |College grads)

=(0.72+0.48-0.48*0.5) =0.96