The table shows the probabilities of a response of chocolate or vanilla when asking a child or adult. Use the formula for conditional probability to determine independence.
a. Are the events "Chocolate" and "Adults" independent? Why or why not?
b. Are the events "Children" and "Chocolate" independent? Why or why not?
c. Are the events "Vanilla" and "Children" independent? Why or why not?
a. Are the events "Chocolate" and "Adults" independent? Why or why not?
If independent.... P (Chocolate l Adult ) = P(Chocolate and Adult) /P(Chocolate)
.21/ (.21 + .39 + .60) = .21/ .35 ???
.21 = .60 ???? not independent
b. Are the events "Children" and "Chocolate" independent? Why or why not?
P(Children l Chocolate) = P(Children and Chocolate) / P(Children) ???
.14/ (.14+ .21+ .35) = .14 / .40 ???
.20 = .35 ??? not independent
c. Are the events "Vanilla" and "Children" independent? Why or why not?
P(Vanilla l Children) = P(Vanilla and Children) / P(Vanilla) ???
.26 / ( .14 + .26 + .40) = .26 / .65 ???
.325 = .40 ??? not independent