Plssssss help10-5?????
2 answers:
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Answer:
P = 0.008908
Step-by-step explanation:
The complete question is:
The table below describes the smoking habits of a group of asthma sufferers
Nonsmokers Light Smoker Heavy smoker Total
Men 303 35 37 375
Women 413 31 45 489
Total 716 66 82 864
If two different people are randomly selected from the 864 subjects, find the probability that they are both heavy smokers.
The number of ways in which we can select x subjects from a group of n subject is given by the combination and it is calculated as:
Now, there are 82C2 ways to select subjects that are both heavy smokers. Because we are going to select 2 subjects from a group of 82 heavy smokers. So, it is calculated as:
At the same way, there are 864C2 ways to select 2 different people from the 864 subjects. It is equal to:
Then, the probability P that two different people from the 864 subjects are both heavy smokers is:
a.
is a proper joint density function if, over its support, is non-negative and the integral of
is 1. The first condition is easily met as long as
. To meet the second condition, we require
b. Find the marginal joint density of and
by integrating the joint density with respect to
:
Then
c. This probability can be found by simply integrating the joint density: