CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 7. Sampling Distributions and Estimations

TABLE7.8:(continued)

Larger Number,x Probability,p

Total 1

When you roll the two die, what is the probability that the sum of the two die is 4? The probability that the sum of
the two die is four is 363.

What is the probability that the larger number is 4? The probability that the larger number is four is 367.

Example:

The Regional Hospital has recently opened a new pulmonary unit and has released the following data on the
proportion of silicosis cases caused by working in the coal mines. Suppose two silicosis patients are randomly
selected from the large population with the disease.

TABLE7.9:

Silicosis Cases Proportion

Worked in the mine 0. 80

Did not work in the mine 0. 20

There are four possible outcomes for the two patients. With ’yes’ representing “worked in the mines” and ’no’
representing “did not work in the mines”, the possibilities are

TABLE7.10:

First Patient Second Patient

1 No No

2 Yes No

3 No Yes

4 Yes Yes

The patients for this survey have been randomly selected from a large population and therefore the outcomes are
independent. The probability for each outcome can be calculated by applying this rule:

P(no for 1st)·P(no for 2nd) = ( 0. 2 )( 0. 2 ) = 0. 04

P(yes for 1st)·P(no for 2nd) = ( 0. 8 )( 0. 2 ) = 0. 16

P(no for 1st)·P(yes for 2nd) = ( 0. 2 )( 0. 8 ) = 0. 16

P(yes for 1st)·P(yes for 2nd) = ( 0. 8 )( 0. 8 ) = 0. 64

IfXrepresents the number of mine workers in this random sample, then the first of these outcomes results inX=0,
the second and third each result inX=1 and the fourth results inX=2. Because the second and third outcomes are
disjoint, their probabilities can be added. The probability distribution ofXis given in the table below:

TABLE7.11:

x Probability ofx

0 0. 04

1 0. 16 + 0. 16 = 0. 32

2 0. 64