I am considering buying 100 NS&I premium bonds, in the UK. Each $1 bond is automatically entered into a draw with a 1 in 30000 chance to win back what is effectively an interest payment*. My questions are:
A) What is my chance to win with 100 bonds?
B) Assuming I buy 100 more bonds each months for 12 months, how much do my chance to win increase month by month?
Edited to reflect commentary from @CactusCake:
Note that purchasing NS&I Premium Bonds is not really gambling in the traditional sense. This is offered as a savings account in the UK. Any time you would like to make a withdrawal, your bonds can be sold back for 1GBP each (same as purchase price). Instead of paying traditional interest to all account holders, the "pool" of everyone's bonds earns interest each month and that sum is then raffled off in chunks to a randomly selected subset of all account holders. Since your initial stake is never at risk, it isn't really a gamble.
See more here: https://www.nsandi.com/premium-bonds.