Notice: This page requires JavaScript to function properly.
Please enable JavaScript in your browser settings or update your browser.
Lære Challenge: Solving the Task Using Bayes' Theorem | Probability of Complex Events
Probability Theory Basics

Sveip for å vise menyen

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.

Oppgave

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)}

Løsning

Switch to desktopBytt til skrivebordet for virkelighetspraksisFortsett der du er med et av alternativene nedenfor
Alt var klart?

Hvordan kan vi forbedre det?

Takk for tilbakemeldingene dine!

Seksjon 2. Kapittel 6

Spør AI

expand
ChatGPT

Spør om hva du vil, eller prøv ett av de foreslåtte spørsmålene for å starte chatten vår

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.

Oppgave

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)}

Løsning

Switch to desktopBytt til skrivebordet for virkelighetspraksisFortsett der du er med et av alternativene nedenfor
Alt var klart?

Hvordan kan vi forbedre det?

Takk for tilbakemeldingene dine!

Seksjon 2. Kapittel 6
Switch to desktopBytt til skrivebordet for virkelighetspraksisFortsett der du er med et av alternativene nedenfor
Vi beklager at noe gikk galt. Hva skjedde?
some-alt