In tennessee pick 3 game you pay .50 cents to select a sequence of 3 digits such 911. If you play this game?

Question

everyday find the probability of winning exactly once in 365 days.

Answer 1

you have a 1/1000 probability of winning on any given day.

P(win at least once) = 1 - P(never win)

= 1 - (1 - 1/1000)^365

= 0.3059301

you have a probability of 30.6% that you will win at least once in the 365 days.

Answer 2

Assuming random digits selected for the winning number each night, you have a 0.001 chance of winning on any night.  To win exactly once the probability is 365*0.001*0.999^364, which is 25.36%.  The probability of never winning is 69.41%, by the way.