Question

P(A1 ∩ A2 ∩ A3 | A1 ∪ A2 ∪ A3) = Explain this probability in words. This is the probability that the firm is awarded at least one of the projects. This is the probability that the firm is awarded projects 1, 2, and 3. If the firm is awarded at least two of the projects, this is the chance that they will be awarded all three projects. If the firm is awarded at least one of the projects, this is the chance that they will be awarded all three projects.

Answer 1

If the firm is awarded at least one of the projects, this is the chance that they will be awarded all three projects.

Explanation:

Remember that when you talk about intersections you include everything, then for this case the intersection of A1,A2,A3 means that all three projects were awarded.

Remember that if an element belongs to only one of the sets of a union, then the element belongs to the union, that is why for the conditional part of the probability event is true that the firm is awarded at least one of the projects.