00:01
For these questions, we are calculating binomial probabilities.
00:07
If we have an exact value that we're looking for, so the probability that x is equal to some specific number, we will use the binomial pdf feature on a calculator.
00:19
And if we are looking for the probability that x is less than or equal to some value, we will use the binomial cdf feature on a calculator.
00:29
So for question nine, we are told that an agent sells life insurance policies to five equally aged healthy people.
00:40
According to recent data, the probability of a person living in these conditions for 30 years or more is two -thirds.
00:47
Calculate the probability that after 30 years and you have three parts.
00:52
So it is important to note that we are dealing with five people and that the probability that we're giving, is two -thirds.
01:13
So question a says to calculate the probability that after 30 years, all five people are still living.
01:21
So the probability that x is equal to five.
01:32
We'll set up our binomial pdf.
01:44
We have five people.
01:46
We have a probability of two -thirds.
01:52
And we're looking for all five people to to still be alive after those 30 years.
01:58
And when we work that out, we get a probability of 0 .132.
02:07
For question b, it says the probability that at least three people are still living.
02:16
So the probability that x is at least three.
02:21
So here it's important to notice that we can use binomial cdf when we're dealing with a less than or equal to, not when we're dealing with a greater than or equal to.
02:31
However, we can rewrite this.
02:35
If we're counting three people, four people, or five people, that means we're not counting two people, one person, or zero people.
02:44
So the probability that x is greater than equal to three is the same as one minus the probability that x is less than or equal to two.
02:56
And that's important because we can use our binomial cdf to calculate that probability that x is less than or equal to two.
03:09
So here we will have one minus.
03:13
And if i want to calculate that probability, i'm going to use binomial cdf, where i have five people.
03:27
My probability is two -thirds, and i'm looking at two or less...