00:01
In this problem, it is said that the probability that a certain make of car will need repairs in the first four months is 0 .2.
00:07
A dealer sells seven such cars, and we need to find the probability that at least one of them will require repairs in the first four months.
00:14
Now, first of all, let us consider r to be the event that the car requires repairs in the first four months, and the probability of this event r is 0 .2, according to the question.
00:25
From here, we can find p of r complement, the probability that the car does not require repairs, and using the complement rule of probability, this is equal to 1 minus p of r.
00:33
So that is 1 minus 0 .2, which is equal to 0 .8.
00:38
Now, what we have been asked to determine is the probability that at least one car requires repairs in the first four months.
00:47
Using the complement rule of probability, this is equal to 1 minus the probability of the complementary event.
00:53
And the complementary event of at least one car requiring repairs is that none of the cars require repairs.
00:58
So none of them require repairs.
01:00
That means the first car does not require repairs and the second car does not require repairs and so on until we get to the seventh car, which also does not require repairs.
01:10
Now, these events are all independent events because whether or not one car requires repairs does not affect in any way or form whether or not the other cars require repairs...