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Leer Challenge: Solving the Task Using Bayes' Theorem | Probability of Complex Events
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Challenge: Solving the Task Using Bayes' Theorem

Situation Description

Imagine a medical study involving two groups of people:

  • Group HH: 750 individuals with heart problems;

  • Group SS: 800 individuals with chronic stomachache.

We know the following about diabetes prevalence:

  • Among group HH, 7% have diabetes — this is the conditional probability P(DH)=0.07P(D∣H)=0.07, meaning the probability that a person has diabetes (DD) given they have a heart problem (HH);

  • Among group SS, 12% have diabetes — this is P(DS)=0.12P(D∣S)=0.12, the probability of diabetes given stomachache.

Here, the letters represent:

  • HH: event "person has a heart problem";

  • SS: event "person has a stomachache";

  • DD: event "person has diabetes".

We want to analyze the overall population formed by these two groups combined.

Taak

Swipe to start coding

  1. Calculate P(H)P(H), the probability that a randomly selected person (from both groups combined) has a heart problem.
  2. Calculate P(S)P(S), the probability that a randomly selected person has a stomachache.
  3. Calculate P(D)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(SD)=P(DS)×P(S)P(D)P(S∣D)= \frac{P(D∣S) \times P(S)}{P(D)}

Oplossing

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Sectie 2. Hoofdstuk 6

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book
Challenge: Solving the Task Using Bayes' Theorem

Situation Description

Imagine a medical study involving two groups of people:

  • Group HH: 750 individuals with heart problems;

  • Group SS: 800 individuals with chronic stomachache.

We know the following about diabetes prevalence:

  • Among group HH, 7% have diabetes — this is the conditional probability P(DH)=0.07P(D∣H)=0.07, meaning the probability that a person has diabetes (DD) given they have a heart problem (HH);

  • Among group SS, 12% have diabetes — this is P(DS)=0.12P(D∣S)=0.12, the probability of diabetes given stomachache.

Here, the letters represent:

  • HH: event "person has a heart problem";

  • SS: event "person has a stomachache";

  • DD: event "person has diabetes".

We want to analyze the overall population formed by these two groups combined.

Taak

Swipe to start coding

  1. Calculate P(H)P(H), the probability that a randomly selected person (from both groups combined) has a heart problem.
  2. Calculate P(S)P(S), the probability that a randomly selected person has a stomachache.
  3. Calculate P(D)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(SD)=P(DS)×P(S)P(D)P(S∣D)= \frac{P(D∣S) \times P(S)}{P(D)}

Oplossing

Switch to desktopSchakel over naar desktop voor praktijkervaringGa verder vanaf waar je bent met een van de onderstaande opties
Was alles duidelijk?

Hoe kunnen we het verbeteren?

Bedankt voor je feedback!

Sectie 2. Hoofdstuk 6
Switch to desktopSchakel over naar desktop voor praktijkervaringGa verder vanaf waar je bent met een van de onderstaande opties
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