how to calculate total chance of winning with diffirent odds

Question

so I wanted to know is there any way to calculate what my total chance of winning say a giveaway if I enter multiple giveaways. as an example i mean say i join 10 giveaways I want to know is there a way to calculate what would be the chance that I won at least one of those 10. specifically when each giveaway has different odds of winning. so for example give away 1 had 10% 2 had 20% 3 had 30% 4 had 40% 5 had 50% 6 had 60% 7 had 70% 8 had 55% 9 had 20% and 10 had 30%. so basically what how do you calculate the chance of a person winning at least one giveaway when they entered multiple ones with different possibilities of success

Answer 1

If you want the odds of at least one win, it is easier in this case to find the odds of winning none of the contests since. $$1-P(wins=0)=P(wins>0)=P(wins>=1)$$ This is easily found as it is just the product of the probability of losing each sweepstakes. So for your example, it would be $$P(wins=0)= (.9)*(.8^2)*(.7^3)... $$