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bookChallenge: 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(D∣H)=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(D∣S)=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.

Compito

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  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(S∣D)=P(D∣S)×P(S)P(D)P(S∣D)= \frac{P(D∣S) \times P(S)}{P(D)}

Soluzione

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Sezione 2. Capitolo 6
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bookChallenge: 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(D∣H)=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(D∣S)=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.

Compito

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(S∣D)=P(D∣S)×P(S)P(D)P(S∣D)= \frac{P(D∣S) \times P(S)}{P(D)}

Soluzione

Switch to desktopCambia al desktop per esercitarti nel mondo realeContinua da dove ti trovi utilizzando una delle opzioni seguenti
Tutto è chiaro?

Come possiamo migliorarlo?

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Sezione 2. Capitolo 6
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bookChallenge: Solving the Task Using Bayes' Theorem

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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(D∣H)=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(D∣S)=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.

Compito

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(S∣D)=P(D∣S)×P(S)P(D)P(S∣D)= \frac{P(D∣S) \times P(S)}{P(D)}

Soluzione

Switch to desktopCambia al desktop per esercitarti nel mondo realeContinua da dove ti trovi utilizzando una delle opzioni seguenti
Tutto è chiaro?

Come possiamo migliorarlo?

Grazie per i tuoi commenti!

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