Foreign Key Versus Table Index

Hi, I'm slightly confused about foriegn keys and indexes on mysql innodb tables. Foreign key constraints create a reference between two tables and indexes make queries on a particular table faster if the index is on a field in the where or order by clause. My question was whether say for the following two tables:

Person                                 Car

Id                                       Id
Name                                 PersonId
Address                              Make
Phone Number                   Colour

If I create a foriegn key linking the id field in person and the personid field in car, do I need to create another index in car table specifically for the personid field if I was running a query such as: "SELECT Id FROM car WHERE personid={personkeynumber}"? Thanks for your help. Jemma