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# Maths question - Help! watch

1. A hospital uses an test that gives the following results:

For a patient who really has cancer, the test is positive 97% of the time.

For a patient who does not have cancer, the test is positive 2% of the time (‘false positive’).

Let’s say that 1% of all patients have cancer.

If Mr Smith has a test, and the result comes back negative, what is the chance that he really is cancer-free?
A hospital uses an test that gives the following results:

For a patient who really has cancer, the test is positive 97% of the time.

For a patient who does not have cancer, the test is positive 2% of the time (‘false positive’).

Let’s say that 1% of all patients have cancer.

If Mr Smith has a test, and the result comes back negative, what is the chance that he really is cancer-free?
Ugh my stats is rusty.

This is one of those "What is the probability of A given B"

Let A be the probability of not having cancer. Let B be the probability of having a negative test.

To get you just multiply the probability of not getting cancer by the probability of getting a negative test from that.
It's helpful to draw a probability tree diagram for this.

The probability of not getting cancer is 0.99 (99%). If you don't have cancer, the probability of getting a negative result is 0.98 (1-0.02).
Spoiler:
Show
Therefore
To get you need to find the ways to get a negative test. We already found way which is to not get cancer and to get a negative test. The other way is to have cancer and then get a negative test.
Again a probability tree diagram is helpful.
Spoiler:
Show
Therefore
Now plug it into the equation.

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Updated: February 28, 2016
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