Question

A test for ovarian cancer has a 2% rate of false positives (i.e. 2% of women...

A test for ovarian cancer has a 2% rate of false positives (i.e. 2% of women who don’t actually have ovarian cancer test positive) and a 0% rate of false negatives.   Data collected by the Cancer association estimates that 1 in every 2500 women over 35 years of age having ovarian cancer. Answer the following questions. [All numeric answers should be accurate to 6 decimal places]

  1. What is the probability that a randomly selected woman over the age of 35 has ovarian cancer?
  2. Is your answer in a) subjective, empirical or classical?   Justify your answer.
  3. What is the probability that a woman over 35 does not have ovarian cancer?
  4. What is the probability that a woman over 35 does not have ovarian cancer and tests positive?
  5. What is the probability of a woman over 35 testing positive for ovarian cancer?
  6. If a woman over 35 tests positive for ovarian cancer, what is the probability that she actually has cancer?
  7. Are i) having ovarian cancer and ii) testing positive for ovarian cancer independent? Explain your answer: use the comparison of two probabilities from this problem setting as part of your explanation.
Math   Statistics-And-Probability   
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Answer #1

P(Positive|Not diseased)=0.02

P(Negative|Not diseased)=0.00

P(Diseased)=1/2500

a)

What is the probability that a randomly selected woman over the age of 35 has ovarian cancer?

=1/2500

B)

Is your answer in a) subjective, empirical or classical? Justify your answer.

Empirical. These probabilities are found by dividing the number of times an event occurred in an experiment by the total number of trials or observations.

C)

What is the probability that a woman over 35 does not have ovarian cancer?

1- 1/2500=2499/2500

D)

What is the probability that a woman over 35 does not have ovarian cancer and tests positive?

P(Positive|Not diseased)=0.02

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