Maybe it’s just late but I seem to be confusing some of the basics of probablility. For example if the event is the probability of a six appearing in 4 throws of a dice then shouldnt the outcome be (1/6)^4.
However if we use the laws of probability where the P(Event)=1-P(Not event) then the number got from 1-(5/6)^4 does not match with the first method.
It’s late in my defense but what am I missing here?
I am wondering why it is differs from the first. The probability of a six rolling in one die is 1/6. So with 4 attempts the value of (1/6)^4 should give the same outcome as the second method but it is not.
(1/6) gives the probability that only a six is rolled. So (1/6)^4 gives the prbabiity that out of 4 rolls, only sixes are rolled. This is incorrect.
You are only looking for the probability that out of 4 rolls, at least one six is is rolled. So the probaiblity that at least one six is rolled, is one minus the porbability that no sixes are rolled. The porbaiblity that no six is rolled on an given roll is 5/6. The probability that no sixes are rolled on 4 rolls is (5/6)^4.
Therefore, the probabiltiy that AT LEAST ONE six is rolled is 1-(5/6)^4.