00:01
This question proposes an experiment and asks us, is it a binomial experiment? the experiment it proposes is like a lottery.
00:10
In a lottery, we choose six numbers at random between 1 and 40.
00:16
So we have 6 numbers between 1 and 40 that we select.
00:22
1 and 40.
00:25
Now, if these numbers match up with the lottery numbers, then that constitutes a success.
00:34
So our question is how many numbers match up with the lottery numbers.
00:40
Now, for this to be a binomial experiment, we need a couple of things.
00:44
We need n individual trials, and each of those trials needs to have an independent and identical probability of success.
00:57
So p is independent and identical.
01:00
That means if i succeed on my first trial or if i fail on my first trial, it does not affect my probability of success on my second trial.
01:17
So let's start looking at this as if it were binomial experiment and say, what would constitute a success, a successful trial? well, a successful trial would be if i selected a lottery number, say the first number i selected, i selected.
01:35
I selected a 3 and the actual lottery number was indeed a 3.
01:44
So say i selected a 3 and the actual lottery number was a 3, if these are equal, then that constitutes a success.
01:51
But say i instead selected a 17 and the actual number was 32, that would not constitute a success because they were not equal.
02:02
So success would be choosing the correct lottery number.
02:06
And since there are 40 to choose from and only one correct, the probability of success here is 1 over 40.
02:16
Now, we have to make sure that there are n trials here and that those trials are independent...