Yes. In particular, as you describe it, you'd then need to solve for P(E1 ∩ E2) by extrapolating from the existing result of P(E2 | E1) present in the article,

Yes. In particular, as you describe it, you'd then need to solve for P(E1 ∩ E2) by extrapolating from the existing result of P(E2 | E1) present in the article, then plug it into that formula you've provided. (Bayes' law streamlines the whole process by combining the two-step calculation into one.) edit: a slight nitpick: E2 is an event ("this person has type A blood"); P(E2) is a number.