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Bob D1
Lv 7
Bob D1 asked in Science & MathematicsMathematics · 9 years ago

What are the chances of death due to disease or from the inoculation ... a probability question?

There is a 1 in 200 chance of death due to the inoculation alone

There is a 1 in 7 chance of death from contracting the disease.

What are the odds of surviving the disease without the inoculation, and what are the odds of surviving with the inoculation?

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I'm not sure how to set this problem up, but here's what I have:

Order of events matters

Death due to inoculation

1 in 200

---------------------

Surving due to inoculation

1 - (1 in 200)

---------------------

Death due to disease

1 in 7

Surviving the disease

1 - (1 in 7)

------------------

I'm using: (n / r) = n! / ((n-r)! r!) = (200 / 1) = 200! / ((200-1)! 1!) = 200 x 199 / (199 x 1) = 200 / 1 = 200

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(n / r) = (7 / 1) = 7! / ((7 - 1)! 1!) = 7 x 6 / (6 x 1) = 7 / 1 = 7

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What is the total probability of death no matter what action you take or don't take?

This seems like it would be a combination of death by inoculation and death by disease:

( 200 / 1) x (7 / 1) = 1,400 / 1 = 1,400

Thus, if you contracted the disease and also took the inoculation, you would have a 1 in 1,400 chance of dying anyway.

Does that seem reasonable? Or, am I on the wrong track?

Best regards

Update:

Thanks Nick for the info.

Yes, just as the question says that even with getting the inoculation there is still a small chance of dying from the inoculation itself. This is true, for example, with rabies vaccines. I was told that if they gave the patient rabies shots and the person didn't already have rabies, there was like a 2% chance that the shots themselves would cause rabies to occur. Of course, there are many factors involved in that scenario.

1 Answer

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  • Nick S
    Lv 6
    9 years ago
    Favorite Answer

    Unless you've left out some information, the problem is

    much simpler than you imagine.

    The order of events is fixed: you first make the decision

    whether to take the inoculation.

    If yes, then you do or don't die from it, but you don't contract the disease.

    If no, then you contract the disease and you do or don't die from it.

    There are two unstated assumptions, both of which are false in the real world:

    1. If you're inoculated, then you don't contract the disease.

    2. If you're not inoculated, then you will contract the disease.

    .....(In this case, you will die with prob 1/7.)

    So the prob of surviving the disease without the inoculation is 6/7 (odds are 6:1),

    and the prob of surviving the inoculation is 199/200 (odds are 199:1).

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