CK-12 Probability and Statistics - Advanced

http://www.ck12.org Chapter 4. Discrete Probability Distribution

Forx=2, only two will pass the test. This event has six simple events:

{SSFF, SFSF, SFFS, FSSF, FSFS, FFSS}

Each of these events has a probability of(. 1 )^2 (. 9 )^2 so

p(x= 2 ) = 6 [(. 1 )^2 (. 9 )^2 ] = 0. 0486

This is a chance of 4.86% that two will pass the test.

Similarly,

p(x= 3 ) = 4 [(. 1 )^3 (. 9 )] = 0. 0036

p(x= 4 ) = (. 1 )^4 = 0. 0001

To summarize, we show all the probability distributions in tabular and graphical forms:

x p(x)

0 65 .61%

1 29 .16%

2 4 .86%

3 0 .36%

4 0 .01%

Figure:The Probability Distribution in Table Form of the Binomial Experiment in this Example (Four Adults who
take a Fitness Test).

Note:p( 4 )is too small to show on the graph.

In the table above, we displayed the probability distribution of random variablex−the number of people, out of 4,
who will pass the fitness test. Although the work done to get the probability distribution is quite involved, it is rather
simple compared to most practical situations. Imagine if our sample was not 4 but 100. In this case, there would be