In a game where a guy has a 20% win probabiliy in each round. What’s the probabiliy for him to win at least one time after six attempts? It can’t be 120%. I know there is a way to calculate this but idk.
In: Mathematics
Probabilities are usually multiplicative. Additionally, when you’re dealing with “at least”, it tends to be better to work out the opposite.
For example, you could figure out the odds of winning game 1, and then add that to the odds of losing game 1 but winning game 2, and then the odds of losing games 1 and 2 but winning game 3, and so on. Or, instead, you could ask “What are the odds of losing 6 games?”
If the odds of losing one game are 80%, then the odds of losing two games are 80% x 80%, or 64%. Do this for 6 games, 80%^(6), you’ll find that the odds of losing 6 games are 26.2%. Therefore, the odds of winning at least one game in 6 are 73.8%.
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