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)Løsning
Tak for dine kommentarer!
single
Spørg AI
Spørg AI
Spørg om hvad som helst eller prøv et af de foreslåede spørgsmål for at starte vores chat
Awesome!
Completion rate improved to 3.85
Challenge: Solving the Task Using Bayes' Theorem
Stryg for at vise menuen
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)Løsning
Tak for dine kommentarer!
Awesome!
Completion rate improved to 3.85single