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Assume a test for cancer correctly identifies 98% of the people tested who do have cancer. Unfortunately, the test gives a false positive reading 1.5% of the time. (A false positive is when the test says you have cancer, but you actually do not.) Millions of people are tested and 0.6% actually have cancer. Find the probability that a person with a positive test result has cancer

Respuesta :

Answer:

0.2828.

Step-by-step explanation:

From the information given:

  • =98%=0.98
  • P(Positive|No Cancer)=1.5%=0.015
  • P(Cancer)=0.6%=0.006

Therefore: P(No Cancer)=1-P(Cancer)=1-0.006=0.994

We want to determine the probability that a person with a positive test result has cancer. i,e. P(Cancer|Positive)

Using Bayes Theorem for Conditional Probability

[tex]P(Cancer|Positive)=\dfrac{P(Positive|Cancer)P(Cancer)}{P(Positive|Cancer)P(Cancer)+P(Positive|No Cancer)P(No Cancer)}\\=\dfrac{0.98X0.006}{0.98X0.006+0.015X0.994}[/tex][tex]P(Cancer|Positive)=0.2828[/tex]

Therefore, the probability that a person with a positive test result has cancer is 0.2828.

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