How is the selection of queen and male bees determined?

Also, do the workers consist of both sexes or only one?How is the selection of queen and male bees determined?
First of all the workers are all female. The queen lives a long time but when her egg supply drops and the workers know she is failing they will make one cell near the top of the hive an an egg is laid in it. The egg hatches and forms a larva which is fed special food (called royal jelly) that turns that larva into a queen. One of the queens leaves the hive taking some of the workers with her and they start a new hive. The drones (male bees) come from extra large cells and are fed differently so they turn into drones. They do no work. Their only purpose is to breed with a queen.How is the selection of queen and male bees determined?
almost right, except the males are hatched from unfertilized eggs, they get the same food as the developing workers, females come from fertilized eggs and males all come from unfertilized eggs. the queen chooses which she will produce.