00:01
So, in this question, we are told that a company takes out an insurance policy to cover accidents that occur as manufacturing plant, and that the probability that one or more accidents will occur in any given month is 0 .11, right? so you can say that the probability of one or more, or like at least one occurring, is equal to 0 .11.
00:22
Okay? we are also told that the number of accidents that occur in any given month is independent of the number of accidents that occur in all other months, right? so it means that this probability applies to all possible months.
00:41
Okay? what we're supposed to do here is to calculate the probability that there will be at least four months in which no accidents occur before the fourth month, in which at least one accident occurs.
00:53
Okay? so what we need to know in order to be able to answer this question is our multiplication rule of counting, right? we know that if i were to tell you that we have a ways to do one thing and b ways to do another thing, and these two things that we're doing are independent of each other, then the number of ways we can do both a and b things is equal to a times b.
01:18
We also know that the same rule applies to probability, meaning that if you're looking for the probability that two events occur, and these two events are independent, then we can find the probability of them happening by multiplying their individual probabilities together, right? so that's going to be useful here, because we're told that the probability of a company, sorry, the probability of an accident occurring during a given month in this company is independent of all the other months.
01:43
Okay? so what this is telling us is that we can treat these as independent events.
01:49
It means that we can use our multiplication rule of counting.
01:53
So if we know that the probability that at least one accident occurs is 0 .11, then it implies that the probability that no accidents occur, so we can call that p of n, is going to be equal to 1, minus 0 .11, right? because we know that the probability that there are no accidents is going to be a complement to the event that there's at least one accident.
02:18
Okay? and so we know that that's going to be 0 .89, okay? so now that we have that in mind, we have to think of our scenario, right? we're given four months, and we know that we want to multiply all of these events together...