Challenge: Solving the Task Using Bayes' Theorem
Situation Description
Imagine a medical study involving two groups of people:
- Group H: 750 individuals with heart problems;
- Group S: 800 individuals with chronic stomachache.
We know the following about diabetes prevalence:
- Among group H, 7% have diabetes — this is the conditional probability P(D∣H)=0.07, meaning the probability that a person has diabetes (D) given they have a heart problem (H);
- Among group S, 12% have diabetes — this is P(D∣S)=0.12, the probability of diabetes given stomachache.
Here, the letters represent:
- H: event "person has a heart problem";
- S: event "person has a stomachache";
- D: event "person has diabetes".
We want to analyze the overall population formed by these two groups combined.
Swipe to start coding
- Calculate P(H), the probability that a randomly selected person (from both groups combined) has a heart problem.
- Calculate P(S), the probability that a randomly selected person has a stomachache.
- Calculate P(D), the probability that a randomly selected person has diabetes.
Finally, use Bayes’ theorem to calculate the probability that a randomly selected person with diabetes has a chronic stomachache, expressed as:
P(S∣D)=P(D)P(D∣S)×P(S)Lösning
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Challenge: Solving the Task Using Bayes' Theorem
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Situation Description
Imagine a medical study involving two groups of people:
- Group H: 750 individuals with heart problems;
- Group S: 800 individuals with chronic stomachache.
We know the following about diabetes prevalence:
- Among group H, 7% have diabetes — this is the conditional probability P(D∣H)=0.07, meaning the probability that a person has diabetes (D) given they have a heart problem (H);
- Among group S, 12% have diabetes — this is P(D∣S)=0.12, the probability of diabetes given stomachache.
Here, the letters represent:
- H: event "person has a heart problem";
- S: event "person has a stomachache";
- D: event "person has diabetes".
We want to analyze the overall population formed by these two groups combined.
Swipe to start coding
- Calculate P(H), the probability that a randomly selected person (from both groups combined) has a heart problem.
- Calculate P(S), the probability that a randomly selected person has a stomachache.
- Calculate P(D), the probability that a randomly selected person has diabetes.
Finally, use Bayes’ theorem to calculate the probability that a randomly selected person with diabetes has a chronic stomachache, expressed as:
P(S∣D)=P(D)P(D∣S)×P(S)Lösning
Tack för dina kommentarer!
Awesome!
Completion rate improved to 3.85single