00:01
We're told that the lifetime risk of developing pancreatic cancer is about 1 in 78, which ends up being about 1 .28%, so it's a probability 0 .128.
00:18
And we're going to sample randomly, n equals 200 people, and we're going to have x be the number of people who developed pancreatic cancer.
00:29
So question, well, a, the first part of this question, and what distribution is this, it's going to be a binomial.
00:39
It's a binomial distribution because we're assuming the, well, it's a fixed number of trials, 200.
00:45
You could either have pancreatic cancer or not.
00:48
And the probability we're going to assume is the same for each and that if they're independent, meaning the chance of one person developing pancreatic cancer does not impact another.
00:59
All right.
01:02
And so there you go.
01:03
These are the parameters we have for our binomial distribution where p is, 1078 and n is 200.
01:10
All right now for part b we want to find the probability that two people will develop pancreatic cancer.
01:18
So the probability that x equals 2.
01:22
So let's get our our function.
01:25
So the probability of x that's the probability of developing pancreatic cancer is binomial that means it has this formula, n choose x times p to the x times 1 minus p to the x times 1 minus p to the n minus x and here n is 200 so this becomes 200 choose x times p which is 0 .0128 to the x times 1 minus 0 .0128 to the 20 minus x okay and for probability of x being 2 what we do is we substitute to and for x.
02:22
So this becomes a two, this becomes a two, and this becomes a two.
02:28
And then what we end up with is 0 .254.
02:42
And we'll round to three decimals.
02:45
All right.
02:45
And then part c has us to find the probability that more than three people will develop pancreatic cancer, that x is greater than three.
02:57
Well, we can think about this as one minus the probability that x is less than or equal to three, meaning three or less, one minus three or less.
03:08
Three or fewer, i should say.
03:11
And then this piece, x is less than or equal to three, is given as the probability of zero plus the probability of one, plus the probability of two, plus the probability of 3.
03:27
All right, so what i've done is use my spreadsheet to figure out all these values, and that's what this little printout is right here.
03:47
So this is the probability for x of 0, 1, 2, 3, 4, 5, 6...