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Lära 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.

Uppgift

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)}

Lösning

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Var allt tydligt?

Hur kan vi förbättra det?

Tack för dina kommentarer!

Avsnitt 2. Kapitel 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.

Uppgift

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)}

Lösning

Switch to desktopByt till skrivbordet för praktisk övningFortsätt där du är med ett av alternativen nedan
Var allt tydligt?

Hur kan vi förbättra det?

Tack för dina kommentarer!

Avsnitt 2. Kapitel 6
Switch to desktopByt till skrivbordet för praktisk övningFortsätt där du är med ett av alternativen nedan
Vi beklagar att något gick fel. Vad hände?
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