Question

According University of Maryland records, 0.65 of undergraduate students have lived in Maryland, 0.39 of undergraduate students have lived in states other than Maryland, and 0.19 of undergraduate students have not lived in any of the 50 states.

a. Determine the probability an undergraduate student selected at random has lived in either Maryland or an other state.

b. Determine the probability an undergraduate student selected at random has lived in both Maryland and an other state.

c. Determine the probability an undergraduate student selected at random has lived in an other state but not Maryland.

d. Determine the probability an undergraduate student selected at random has lived in Maryland, given they have lived in an other state.

Answer 1

let living in Maryland and other state are denoted by event A and B

a)

probability an undergraduate student selected at random has lived in either Maryland or an other state

P(A u B) =1-P(have not lived in any of 50 states)=1-0.19 =0.81

b)

probability an undergraduate student selected at random has lived in both Maryland and an other state

P(A n B)=P(A)+P(B)-P(A u B) =0.65+0.39-0.81 =0.23

c)

probability an undergraduate student selected at random has lived in an other state but not Maryland

=P(B)-P(A n B) =0.39-0.23 =0.16

d)

probability an undergraduate student selected at random has lived in Maryland, given they have lived in an other state =P(A|B)=P(A n B)/P(B) =0.23/0.39 =0.5897