I think of the difference as:
joint probability: refers to whole sample space
conditional probability: refers to restricted sample space (only among those who satisfy the condition)
However, I encountered this question (which is about constructing a tree diagram) and this really sounds like conditional probability instead of joint probability and would like to ask why this cannot be a conditional probability.
78% of students can construct tree diagrams. Of those who can construct tree diagrams, 97% passed, while only 57% of those students who could not construct tree diagrams passed.
Of those means those who constructed tree diagrams so 'able to construct a tree diagram' should be a condition. However, when calculating this fact is regarded as 'joint probability' that is P(tree diagram = yes AND passed = yes) instead of (passed = yes | tree diagram = yes). Maybe I don't understand English well but that phrase really sounds like conditional probability.
How do I effectively differentiate these two concepts from the sentence?