Question

1) Suppose it is known that 4.09% of the population suffers from a particular disease. A...

1) Suppose it is known that 4.09% of the population suffers from a particular disease. A blood test has a 87.8% chance of identifying the disease for diseased individuals, but also has a 11.03% chance of falsely indicating that a healthy person has the disease.

If your blood test is positive, what is the chance that you have the disease?

Round your answer to the nearest hundredth.

2)

A ball is chosen at random from a bag containing 205 balls that are either red or blue and either dull or shiny. There are 10 red shiny balls and 93 blue balls.

What is the probability of the chosen ball being shiny conditional on it being red?

Round to the nearest hundredth.

3)

A ball is chosen at random from a bag containing 214 balls that are either red or blue and either dull or shiny. There are 9 red shiny balls and 119 blue balls.

What is the probability of the chosen ball being dull conditional on it being red?

Round to the nearest hundredth.

4)

Suppose it is known that 6.9% of the population suffers from a particular disease. A blood test has a 80.26% chance of identifying the disease for diseased individuals, but also has a 7.25% chance of falsely indicating that a healthy person has the disease.

What is the probability that a person will have a positive blood test?

Round your answer to the nearest hundredth.

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