$1$

$.$

$3$

$.$

$1$

$.$

$$Computer programs are classified by the length of the source code and by the execution time. Programs with more than

$1$

$5$

$0$

$$lines in the source code are big

$($

$$

$)$

$.$

$$Programs with

$<=$

$1$

$5$

$0$

$$lines are little

$($

$$

$)$

$.$

$$Fast programs

$($

$$

$)$

$$run in less than

$0$

$.$

$1$

$$seconds$.$ Slow programs

$($

$$

$)$

$$require at least

$0$

$.$

$1$

$$seconds$.$ Monitor a program executed by a computer. Observe the length of the source code and the run time. The probability model for this experiment contains the following information:

$$

$[$

$$

$$

$]$

$=$

$0$

$.$

$5$

$,$

$$

$[$

$$

$$

$]$

$=$

$0$

$.$

$2$

$$and

$$

$[$

$$

$$

$]$

$=$

$0$

$.$

$2$

$.$

$$What is the sample space of the experiment? Calculate the following probabilities:

$($

a

$)$

$$

$[$

$$

$]$

$($

b

$)$

$$