Question

Based on data from Bloodjournal.org, 10% of women 65 years of age and older have anemia, which is a deficiency of red blood cells. In tests for anemia, blood samples from 8 women 65 and older are combined. What is the probability that the combined sample tests positive for anemia? Is it likely for such a combined sample to test positive?

Answer 1

the probability that the combined sample tests positive for anemia is ≈ 0,38.

Thus it is 38% likely that such a combined sample to test is positive.

Explanation:

The combined sample tests positive if at least one of the 8 women has anemia.

Let p be the probability that a women 65 years of age and older have anemia

Then p=0.1

The probability that one of the 8 women has anemia and others does not is:

p×
`p^(7)` .

Since there are 8 combinations of this probability is possible, the probability that at least one of the 8 woman has anemia is:

8×p×
`p^(7)` =8×0.1×
`0.9^(7)` ≈ 0,3826