Probability Quiz Focused on Bayes Theorem

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Description:
Test your understanding of Bayes' Theorem with 10 carefully crafted problems. Each question includes step-by-step explanations to reinforce learning ( PDF Solution ).

Suggested Time Limit: 15-18 minutes.

Quiz prepared by Dr. Raj Popat, Assistant Professor, Department of Agricultural Statistics, Junagadh Agricultural University

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1. A disease affects 1% of a population. A test for the disease is 99% accurate (both sensitivity and specificity). If a person tests positive, what is the probability they actually have the disease?

1 point

A) 50%

B) 75%

C) 90%

D) 99%

Other:

Clear selection

2. In a school, 60% are boys and 40% are girls. 10% of boys wear glasses, and 20% of girls wear glasses. If a randomly chosen student wears glasses, what is the probability they are a girl?

1 point

A) 25%

B) 40%

C) 57.14%

D) 75%

Other:

Clear selection

3. A bag has 3 red and 7 blue marbles. You draw one marble, note its color, and replace it. If you repeat this and the second draw is red, what is the probability the first was also red?

1 point

A) 30%

B) 42.86%

C) 50%

D) 60%

Other:

Clear selection

4. A factory has two machines:

Machine A makes 60% of items, with 5% defective.

Machine B makes 40%, with 10% defective.
If an item is defective, what is the probability it came from Machine B?

1 point

A) 40%

B) 57.14%

C) 66.67%

D) 80%

Other:

Clear selection

5. A fair coin is flipped:

If heads, a red ball is placed in a box.

If tails, either a red or green ball is placed (50% each).
A red ball is drawn. What is the probability the coin was heads?

1 point

A) 33.33%

B) 50%

C) 66.67%

D) 75%

Other:

Clear selection

6. A rare disease affects 0.1% of people. A test is 99% accurate (1% false positives). If a person tests positive, what is the probability they have the disease?

1 point

A) 1%

B) 9%

C) 50%

D) 90%

Other:

Clear selection

7. A spam filter detects 90% of spam emails but also incorrectly flags 5% of non-spam. If 20% of emails are spam, what is the probability an email flagged as spam is actually spam?

1 point

A) 78.26%

B) 81.82%

C) 90%

D) 95%

Other:

Clear selection

8. A medical test for a rare disease is 99% accurate:
* If a person has the disease, the test is positive 99% of the time (true positive rate = 99%).

* If a person does not have the disease, the test is negative 99% of the time (true negative rate = 99%).
Only 1 in 1,000 people in the population has the disease. If a randomly selected person tests positive, what is the probability they actually have the disease?

1 point

A) 10%

B) 50%

C) 90%

D) 9%

Other:

Clear selection

9. A lie detector is 85% accurate when a person lies and 70% accurate when they tell the truth. If 20% of suspects lie, what is the probability a suspect is lying given the detector says they're lying?

1 point

A) 41.16%

B) 51.2%

C) 63.6%

D) 75.8%

Other:

Clear selection

10. A rare cancer affects 0.5% of people. A new test is 99% sensitive (1% false negatives) but only 95% specific (5% false positives). Given a positive result, what is the probability of having cancer?

1 point

A) 9.1%

B) 16.7%

C) 25.3%

D) 50.5%

Other:

Clear selection

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