The correct answer is: TRUE.
Bayes’ theorem is a mathematical formula that is used to calculate the probability of a hypothesis being true given some evidence. The theorem is named after Thomas Bayes, an English mathematician who first published it in 1763.
Bayes’ theorem can be written as follows:
$$P(H|E) = \frac{P(E|H)P(H)}{P(E)}$$
where:
- $P(H|E)$ is the probability of hypothesis $H$ being true given evidence $E$.
- $P(E|H)$ is the probability of evidence $E$ given hypothesis $H$.
- $P(H)$ is the probability of hypothesis $H$ being true.
- $P(E)$ is the probability of evidence $E$.
Bayes’ theorem can be used to calculate the probability of a hypothesis being true given some evidence. For example, if we know that the probability of a person having a certain disease is 0.1, and we know that the probability of a person with that disease having a certain symptom is 0.9, then we can use Bayes’ theorem to calculate the probability that a person with that symptom has the disease.
Bayes’ theorem can also be used to update our beliefs about a hypothesis as we receive new evidence. For example, if we initially believe that the probability of a hypothesis being true is 0.5, and we then receive evidence that makes the hypothesis more likely, we can use Bayes’ theorem to update our belief to a higher probability.
Bayes’ theorem is a powerful tool that can be used to make inferences about the world around us. It is used in a variety of fields, including statistics, machine learning, and decision analysis.