I can understand the table, but I cannot figure out how to solve it when they have removed the $M$.
I know that $L = \text{false}$ is $30\%$ since $L = \text{true}$ is $70\%$, but how to find out the $V = \text{false}$? Is there some formula for this or can it be done without?
The answer should be: d) 0.925
Let F be false and T be true. Using the total law of probability, we can show that $P(V=F|L=F)$ is:
$$P(V=F|L=F,M=T)P(M=T)+P(V=F|L=F,M=F)P(M=F) \space ...(1)$$ $$=(1-0.3)(0.1)+(1-0.05)(0.9)$$ $$=\frac 7{100}+ \frac {171}{200}= \frac {185}{200}=0.925$$
In $(1)$ I used the fact that $$P(V=F|L=F,M=T)=1-P(V=T|L=F,M=T)$$ and $$P(V=F|L=F,M=F)=1-P(V=T|L=F,M=F)$$ Please let me know if I can clarify anything.