Conditional Probability & Bayes Rule Quiz

In the previous section, you found the following proportions from the cancer results dataset.

• Patients with cancer: 0.105
• Patients without cancer: 0.895
• Patients with cancer who tested positive: 0.905
• Patients with cancer who tested negative: 0.095
• Patients without cancer who tested positive: 0.204
• Patients without cancer who tested negative: 0.796

Based on the above proportions observed in the data, we can assume the following probabilities.

Probability	Meaning
P(cancer) = 0.105	Probability a patient has cancer
P(~cancer) = 0.895	Probability a patient does not have cancer
P(positive|cancer) = 0.905	Probability a patient with cancer tests positive
P(negative|cancer) = 0.095	Probability a patient with cancer tests negative
P(positive|~cancer) = 0.204	Probability a patient without cancer tests positive
P(negative|~cancer) = 0.796	Probability a patient without cancer tests negative

Quiz Questions

Use the probabilities given above and Bayes rule to compute the following probabilities.

1. Probability a patient who tested positive has cancer, or P(cancer|positive)
2. Probability a patient who tested positive doesn't have cancer, or P(~cancer|positive)
3. Probability a patient who tested negative has cancer, or P(cancer|negative)
4. Probability a patient who tested negative doesn't have cancer, or P(~cancer|negative)

Then, use the Jupyter notebook to compare them to true proportions in the dataset.

QUIZ QUESTION::

Using the probabilities above and Bayes rule, compute the following probabilities.

ANSWER CHOICES:

0.658

0.342

0.236

0.389

0.674

0.986

0.014

Probability	Value
P(cancer|positive)
P(~cancer|positive)
P(cancer|negative)
P(~cancer|negative)

SOLUTION:

Probability	Value
P(~cancer|positive)	0.658
P(cancer|positive)	0.342
P(~cancer|negative)	0.986
P(cancer|negative)	0.014

Do these proportions match with the probabilities you computed earlier?

Yes

No

SOLUTION:

Yes