00:01
All right, for your question, you are asked.
00:02
An automobile insurance company predicts that 15 % of policyholders file a claim within the next year.
00:09
Since this company has many policyholders, we may assume the filing a claim is independent between policyholders.
00:17
Part a says that 15 policyholders are randomly selected.
00:20
What is the probability that exactly two will file a claim within the next year? okay, so at this point, i'd like to address what this question type is.
00:30
So if you take a look at some of the information i've written down already, the outcomes we were told are independent, which means the probability is going to stay the same for each trial.
00:42
There are only two possible outcomes.
00:45
They filed a claim or they didn't file a claim.
00:49
And we have a set number of trials.
00:51
We're only going to pick 15 people here for this probability question.
00:56
That leads me to conclude that this is what's called a binomial probability question okay so binomial probability basically what we want to do to solve part a is first figure out how many different ways we can have two claims out of 15 people and what you have to think about is maybe it's your first two people had the claim or maybe it's your first in the fifth person or the first in the 10th person.
01:31
There's a bunch of different ways we can get groups of two out of 15.
01:36
We need to calculate that.
01:39
And to do that, i'm going to use what's called a combination.
01:43
Okay, so we have 15 that we're choosing from.
01:47
We want combinations of two.
01:49
This is basically saying how many unique groups of two.
01:53
Now, this can be performed on a scientific calculator.
01:57
They all have it.
01:58
I'm using a ti -84, and i'll you where it's found.
02:03
I first type in 15, then i hit math, prb, ncr.
02:12
And what i found is that there are 105 different ways to get a group of two out of 15.
02:21
Then i multiply it by the probability of success or filing a claim.
02:27
The original question said that that probability is 15%, or 0 .15.
02:32
So i'm going to multiply by a point 0 .15 and how many claims do we think happened or want to have happened? that's two...