I LOVE THIS BINOMIAL DISTRIBUTION APPLET Click on the "Binomial Calculator" near the top on the right. Set the number of trials at fifty or so, then slowly adjust the probabilty of success. When you can explain what you see, you understand a lot. What will happen when you hold p steady and increase the number of trials. Think about both the mean and std dev. This page also has a good applet for the normal approximation to the binomial.... scroll down the list of applets toward the bottom..
Hyperstats gives the highlights of the Binomial distribution. Spend some time looking at the applets and related pages linked on this page.... some nice stuff.