Not So Ridiculous After All

Caution: (very minor) spoilers for Dracula and Dracula the Undead.

One thing that always bothered me in Dracula was that Lucy was given three blood transfusions, with the three most convenient people as donors, with no question of matching the blood types, with no ill effects. Of course, Stoker couldn't have known that that was a problem, as blood types were discovered shortly after Dracula was published. Indeed, that's a plot point in Dracula the Undead.

But then it occurred to me that depending on your blood type, you might have a pretty chance of a random person being compatible with you. Indeed, if Lucy happened to be AB positive, she could have transfusions from anyone.

So I finally got around to working out the odds of a random person receiving blood transfusions from three different random people, and surviving.

Using some information about distribution of blood types from this page of the NHS Blood and Transplant website, and making the assumptions that that hasn't changed hugely over the past hundred-odd years, and that no-one involved had any rare blood types, I calculated Lucy's chances:

You can receive blood from anyone who doesn't have any of A, B, or Rh that you don't -if you have it and they don't, it's fine.
Add up all of the compatible percentages, and you get the percentage of people who can donate blood to you.
Divide by 100 and you have the probability of a random person being able to donate to you.
Cube that, and the result is the probability of three random people all being able to donate to you.

But that's the probability given that you have a certain blood type, and we don't know Lucy's blood type, so we need to calculate that figure for each blood type, and than calculate:

(probability of having blood type)*(probability of three people being able to donate to blood type)

and add up the results.

I came out with 0.2970, or 30%, to the nearest %, which is not a fantastic chance IRL, but more than plausible enough for fiction, I think.