Question

Consider the following information about passengers on a cruise ship on vacation: 40% check work e-mail, 30% use a cell phone to stay connected to work, 27% bring a laptop with them on vacation, 22% both check work e-mail and use a cell phone to stay connected, and 50% neither check work e-mail nor use a cell phone to stay connected nor bring a laptop. In addition 88% of those who bring a laptop also check work e-mail and 69% of those who use a cell phone to stay connected also bring a laptop. With

E = event that a traveler on vacation checks work e-mail
C = event that a traveler on vacation uses a cell phone to stay connected
L = event that a traveler on vacation brought a laptop

use the given information to determine the following probabilities. A Venn diagram may help. (Round all answers to four decimal places.)

(e)    P(E^cand C^cand L^c ) =

(f)    P(E or C or L) =

(i)    P(E and C and L) =

(l)    P(C|(E and L)) =

Answer 1

P(E )=			0.4
P(C )=			0.3
P(L )=			0.27
P(E n C)=			0.22
P(E u C u L)c=			0.5
P(E| L) =			0.88
P(L|C)=			0.69

e)

P(E^cand C^cand L^c ) = P(E u C u L)^c=0.5

f) P(E or C or L) = 1-P(E^cand C^cand L^c ) =1-0.50 =0.50

i) P(E and C and L) = P(E u C u L)-( P(E)+P(C)+P(L)-P(E n C)-P(L)*P(E|L)-P(C)*P(L|C))

=0.5-(0.4+0.3+0.27-0.22-0.27*0.88-0.3*0.69) =0.1946

j)

P(C|E n L) =0.1946/(0.27*0.88) =0.8190