# Elementary probability theory

Diagnosis tests of medical conditions have several results. The test result can be positive or negative, whether or not a patient has the condition. A positive test(+) indicates the patient has the condition. A negative (-) test indicates that a patient does not have the condition. Remember, a positive test does not prove that the patient has the condition. Additional medical test may be required.Consider a random sample of 200 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown.

Conditions Conditions Row Total

presents Absent

Test results + 110 20 130

Test Results - 20 50 70

Column Total 130 70 200

Assume the sample is representing of the entire population. For a person selected at random, compute the following probabilities.

a) P(+, given condition present);this is known as the sensitivity of a test.

b) P( -, given condition present); this is known as the false-negative rate.

c) P( -, given condition absent); this is known as the specificity of a test.

d) P( +, given condition absent); this is known as the false - positive rate.

e) P( condition presents and +);this a predictive of the test.

f) P( condition presents and - )

https://brainmass.com/statistics/conditional-probability-distribution/201650

#### Solution Preview

Conditions Conditions Row Total

presents Absent

Test results + 110 20 130

Test Results - 20 50 70

Column Total 130 70 200

Assume the sample is representing of ...

Elementary Probability Theory: Botanist Example Problems

Elementary Probability Theory:

A botanist has developed a new hybrid cotton plant that can withstand insects better than other cotton plants. However, there is some concern about the germination of seeds from the new plant.To estimate the probability that a new plant will germination, a random sample of 3000 seeds was planted in warm, moist soil. Of these seeds, 2430 germinated.

a) Use relative frequencies to estimate to estimate the probability that a seed will germinate. What is your estimate?

b) Use relative frequencies to estimate the probability that a seed will not germinate. What is your estimate?

c) Either a second germinates, or it does not. What is the sample space in this problem? Do the probabilities assigned to the sample space add up to 1? Explain.

d) Are the outcomes in the sample space of part (c) equally likely?