00:01
Here, we're told that the probability that a certain type of car will need repairs in the first 8 months is 0 .4, so let's just call that p.
00:10
That's 0 .4.
00:12
And a dealer is going to sell 5 of these kinds of cars, so let's set n equal to 5.
00:19
We want to find the probability that at least one of them will need repairs in the first 8 months.
00:25
First, before we compute this probability, let's recognize what we're doing here as a binomial experiment.
00:31
Let's just recap how binomial experiments work.
00:37
So it's characterized by two parameters, p and n.
00:40
P is the probability of success, which ironically enough in our case means the probability that the car will need repairs in the first 8 months, and n is the number of trials you're doing.
00:52
For us, that's 5, since our dealer is selling 5 of these cars.
00:56
Then, you can define a random variable x, which counts the number of successes you get in your n trials.
01:04
So going back to our problem, we want that the probability of x is greater than 1, since we want the probability that at least one of these 5 cars will need repairs in the first 8 months.
01:17
And now, for a binomial experiment, this x has a probability distribution that is well known.
01:23
Probability that x is equal to k, that you get exactly k successes, is given by the following formula...