The probability that a randomly selected point on the grid below is in the blue area is 9/16
2 answers:
Answer:
The correct option is 1.
Step-by-step explanation:
it is given that the probability of a randomly selected point on the grid below is in the blue area is 9/16.
In the given grid we have only two colors that are blue and white.
Let A be the event of a randomly selected point on the given grid is in the blue area.
If the randomly selected point on the given grid does not lie in the blue area, it means it lies on white area.
We will calculate P(A'), to find the probability that a randomly selected point is in the white on the grid.
We know that the sum of the probability is 1.
It is given that
Therefore option 1 is correct.
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An actual two-by-two table is a tabular representation containing two rows and two columns.
- The columns consist of the tested True positive for prostate cancer and tested True Negative for prostate cancer
- The rows consist of the predicted positive screening and predicted negative values
Mathematically, the set-up of the two-by-two table for this data can be computed as:
Tested True Positive for cancer True Negative Total
Predicted Positive 800 3200 4000
Predicted Negative 100 95900 96000
Total 900 99100 100000
<h3>b)</h3>The prevalence rate of prostate cancer in this population is:
= 9 per thousand.
<h3>c)</h3>
The calculation of the sensitivity of this screening is as follows:
where;
- TP = True positive for cancer
- PN₁ = Predicted Negative for true positive cancer
∴
= 0.889
= 88.9%
The interpretation shows that 88.9% are correctly identified to be actual positive for prostate cancer.
<h3>d)</h3>The calculation of the specificity of this screening is as follows:
where;
- TN = True positive for cancer
- PN₂ = Predicted Negative for true negative cancer
∴
= 0.9677
= 96.77%
The interpretation shows that 96.7% of an actual negative is correctly identified as such.
<h3>e)</h3>
The positive predicted value of the screening test is computed as:
= 0.2
= 20%
The interpretation of the positive predicted value of this screening shows that 20% that are subjected to the diagnosis of positive prostate cancer truly have the disease.
Learn more about tabular representation here: