00:01
So we're looking at driving tests in missouri.
00:04
95 % of people pass on the first attempt.
00:07
So if you take someone who's taking this test, p equals 0 .65, but they pass.
00:14
7 people take it.
00:15
So n equals 7.
00:17
What's the probability that at most 3 of them pass in their first attempt? so that would be the probability that x is at most 3.
00:26
So 3 or less.
00:28
So how do we go about working this on? well, this is a binomial problem.
00:33
A binomial problem has only two outcomes.
00:37
They pass or they don't, and those outcomes are independent for each person.
00:43
So we have a series of independent trials where for each trial, the same probability applies.
00:49
And when we're dealing with binomial, we can use a binomial formula, which is the probability of exactly x successes is n choose x, p to the x, 1 minus p to the n minus x.
01:05
So this is a binomial formula.
01:07
We'll use p of 2 as our example for it.
01:13
This term here, n choose x, is about combinations.
01:17
It's how many ways you have of putting your series of events in order.
01:22
And it's given by n factorial over x factorial, n minus x factorial.
01:28
But a lot of calculators have a button that looks a lot like this, and we'll just do it for you.
01:33
So we have 7 choose 2, which is 21.
01:41
So that's our first term.
01:43
Our second term is for your successes.
01:46
So 0 .65, the chance of passing, to power of 2, for the two people who did pass.
01:51
And then we have the failures.
01:53
0 .35, it's a power of 5 for the 5 people who did not pass.
01:59
So that's how you work out a term...