Finding the probability of given model I'm trying to model a system given as a project, any help or advice is useful for now.
Here our assumptions for a part of it:


*

*If I study for the finals and do assignments, I have $80\%$ chance to get a scholarship

*If I neither do assignments nor study, my chance reduces to $20\%$

*If I either do the assignments or study for the final, I have $60\%$ chance to get a scholarship.

*The chance that I will do assignments or study are both $50\%$.


So, given that I got the scholarship what is the probability that I have did the assignments?
 A: I would suggest drawing a tree diagram to visualize this problem (A = Assignments, F = Finals, S = Scholarship):

The red probabilities at the end of the branches are the products of probabilities leading to these branches. For example for the leftmost branch we have $0.5\times 0.5\times 0.8 = 0.2$.
From this it is easy to calculate the probability: There are four possibilities of getting a scholarship, but only two of those include you having done your assignments (marked with boxes). So the probability of having done the assignments given that you received a scholarship is:
$$
P(A|S) = \frac{0.2+0.15}{0.2+0.15+0.15+0.05}=\frac{0.35}{0.55}\approx 0.636
$$
It is the sum of probabilities of those two branches of the tree where you got scholarship and did the assignments divided by the total sum of probabilities of getting the scholarship.
A: The conditional probability of having done assignments given that you got the scholarship is $35/55\approx0.636$. The probability of having done assignments is $0.5$, as stated by the fourth bullet point.
You have 4 equally likely scenarios a priori:


*

*study + assignments $\rightarrow\, 80\%$ probability of getting the scholarship

*study + no assignments $\rightarrow\, 60\%$ probability of getting the scholarship

*no study + assignments $\rightarrow\, 60\%$ probability of getting the scholarship

*do nothing $\rightarrow\, 20\%$ probability of getting the scholarship


The conditional probability is $P(A|S)=\dfrac{0.8+0.6}{0.8+2\centerdot0.6+0.2}=\dfrac{35}{55}\approx0.636$
