Question

9) The table below describes the smoking habits of a group of asthma sufferers. Light Heavy Nonsmoker smoker smoker Total Men 430 34 40 504 Women 408 49 44 501 Total 838 83 84 1005 If two different people are randomly selected from the 1005 subjects, find the probability that they are both women. Round to four decimal places. 501 - .4985/23.2493 1005

Answer 1

Solution:

Given:

	Nonsmoker	Light Smoker	Heavy Smoker	Total
Men	430	34	40	504
Women	408	49	44	501
Total	838	83	84	1005

Two different people are randomly selected from the 1005 subjects.
We have to find:
P( they are both Women) =.............?

Since two different people are randomly selected from the 1005 subjects, we need to use Combination to find above probability.

Thus we get:

P( they are both Women)

= Number of ways of getting 2 women from 501 women / number of way of getting 2 people from 1005 people

P( they are both Women) = ₅₀₁C₂ / ₁₀₀₅C₂

Where

$_{n}C_{x}= \frac{n!}{x!\times (n-x)!}$

$_{501}C_{2}= \frac{501!}{2!\times (501-2)!} = \frac{501!}{2!\times 499!} = \frac{501 \times 500 \times 499!}{2 \times 1 \times 499!} =125250$

₁₀₀₅C₂ = 1005! / ( 2! x (1005-2)! = 1005! / ( 2! x 1003! ) = 504510

Thus

P( they are both Women) = ₅₀₁C₂ / ₁₀₀₅C₂

P( they are both Women) = 125250 / 504250

P( they are both Women) = 0.248261

P( they are both Women) = 0.2483