I have 2 specific problems, one 'requiring' me to use a probability tree, and the other a Venn diagram. I know that apparently the Venn diagrams can be converted into probability trees and vice versa, so I have attempted to use the probability diagrams for both questions, which wasn't successful. However, I do not know what I am doing wrong and whether I am assuming something which is not actually true, e.g. that certain events are independent. In some questions I am obliged to assume the latter, whereas in others this gives me erroneous results.
38% of the students in a Year 12 IB Mathematics class are female. Of the female students in this class, 13% are left-handed, whereas 24% of the male students are left handed.
a. Find the prob. that a randomly chosen student from this class is left handed. b. Find the prob. that a randomly chosen student is female, given that the student is left-handed.
For this problem, the mark scheme offers a probability diagram: Prob diagram
However, I do not understand why in part a it is assumed that the events 'being female' and 'being left-handed' and 'being male' and 'left handed' are independent (as P(A and B)=P(A)P(B)). (It does seem intuitive though.) But then the part b answer implies that the events 'being female' and 'being left-handed are independent' as P(A given B) doesn't equal P(A). What is going on?
In the town of Expiet, 71% of the population are right-handed. 44% are either right handed or have blonde hair but not both, and 21% do not have blonde hair.
A member of the population is selected at random. Find the likelihood that the person:
a. is right handed but not blonde b. is both right handed and has blonde hair c. is right handed or has the blonde hair
Although the markscheme has used a venn diagram with 4 sets of 4-variable equations, I have attempted to use a prob tree, which was this:
In this case, I know that this tree is clearly wrong, but I dont know why. The 2nd equation evidently gives me the same result as the probability mentioned in the question, so this is weird. Also, I think that I can't assume that each of the right-handed/ non-right handed branch will have the same prob. of being blonde/non-blonde, but I am unsure. So what is the flaw in my reasoning and what is the correct prob. tree diagram?
If someone could clarify the above issues (and perhaps suggest how to convert a Venn diagram into a prob. tree diagram), I would be grateful.