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# Category Archives: Conditional Probability

## Two-Way Table Data Probability problems

**Two Way Table Data Conditional Probability example problem**

When insurance companies establish policies for overing screening tests for diseases, one important factor is the value of the test predicting the disease. For example, for a certain type of disease, insurance companies may only cover the test costs if the test improves the prediction of having the disease by 80%. To help decide coverage policy for a new test, use the following data to help decide whether the test should be covered.

a) Find **P(A)** = P(Having the disease among everyone)

b) Find **P(B)** = P(Testing positive for everyone)

c) Find **P(A and B)** = P(Having the disease and testing positive)

d) Find **P(A | B)** = P(Having the disease given tested positive)

e) Should the test be covered? What is your conclusion? Justify your answer using the conditional probabilities above.

Solution to this Calculus **Two Way Table Data Conditional Probability** practice problem is given in the video below!

## Venn Diagram and Conditional Probability problems

## Venn Diagram Bayes Rule Probability example question

For two events we have P(A) = 0.29, P(B) = 0.43, and P(A B) = 0.65. What is P(A B)?

a) 0.27

b) 0.07

c) 0.16

d) 0.43

e) 0.08

f) none of the above

Solution to this **Venn Diagram Probability** practice problem is given in the video below!

## Venn Diagram Bayes Rule Probability example problem #2

A universal set U = {1, 2, 3, 4, 5, 6, 7, 8} has subsets A = {1, 2, 3, 4} and B = {1, 2, 6, 7}. What set is A’ B?

a)

b) {1, 2, 5, 6, 7, 8}

c) {1, 2, 3, 4}

d) {1, 2, 3, 4, 5, 8}

e) {1, 2}

f) none of the above

Solution to this **Venn Diagram Probability** practice problem is given in the video below!

## Venn Diagram Probability word problem example

A manufactured component has its quality graded on its performance, appearance, and cost. Each of those three characteristics is graded as either pass or fail. There is a probability of 0.40 that a component passes on both appearance and cost. There is a probability of 0.31 that a component passes on all three characteristics. There is a probability of 0.64 that a component passes on performance. There is a probability of 0.19 that a component fails on all three characteristics. There is a probability of 0.06 that a component passes on appearance but fails on both performance and cost.

a) What is the probability that a component passes on cost but fails on both performance and appearance?

b) If a component passes on both appearance and cost, what is the probability that it passes on all three characteristics?

Solution to this **Venn Diagram Probability** practice problem is given in the video below!

## Venn Diagram & Bayes Rule Conditional Probability example question #3

How does VENN Diagram relate to Bayes Formula

when finding Conditional Probability?

Solution to this **Venn Diagram & Bayes Formula Conditional Probability** practice problem is given in the video below!

## Conditional Probability Bayes Rule example problem #4

On Tuesday morning, David randomly picks a microphone, and it fails. What is the probability that the microphone of brand **Y** was chosen, given that probability of failure for microphone **X** is 0.3, probability of failure for microphone **Y** is 0.4, probability of choosing microphone **X** is , and probability of choosing microphone **X** is ?

a)

b)

c)

d)

e)

f) none of the above

Solution to this **Conditional Probability Bayes** practice problem is given in the video below!

## Conditional Probability Bayes Rule example #5

A car brand **X** produces 40% of its cars at plant **A** and the remainder at plant **B**. Of all cars produced at plant **A**, 20% do not have a spare tire, while 30% of the cars produced at **B** do not have a spare tire. Car **X** is purchased, and it happens to have a spare tire. What is the probability that it was produced at plant **B**?

a)

b)

c)

d) 0.7

e) 0.8

f) none of the above

Solution to this **Conditional Probability Bayes** practice problem is given in the video below!

## Conditional Probability Bayes Rule example question #6

David has two microphones which he uses to teach his Algebra class; one is brand **X** and the other is brand **Y**. Microphone **X** fails with probability 0.3, while brand **Y** fails with probability 0.4. On a particular morning, David picks a microphone at random. What is the probability that it will fail?

a) 0.7

b) 0.35

c) 0.12

d) 0.58

e) 0.42

f) none of the above

Solution to this **Conditional Probability Bayes** practice problem is given in the video below!

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