$1\mathrm{.}3\mathrm{.}1.$ Computer programs are classified by the length of the source code and by the execution time. Programs with more than $150$ lines in the source code are big $(B).$ Programs with $150$ lines are little $(L).$ Fast programs $(F)$ run in less than $0\mathrm{.}1$ seconds. Slow programs $(W)$ require at least $0\mathrm{.}1$ 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: $P[LF]=0\mathrm{.}5,P[BF]=0\mathrm{.}2$ and $P[BW]=0\mathrm{.}2.$ What is the sample space of the experiment? Calculate the following probabilities:

$($a$)P[W]$

$($b$)P[B]$

$($c$)P[WB]$