What is the probability for the new instance in the previous exercise?

Question

What is the probability  for the new instance  in the previous exercise?

BlackTom AI · Accepted Answer

The provided data for this item includes only the question text and a single numeric answer, but there are no multiple-choice options to evaluate. Consequently, a step-by-step option-by-option analysis cannot be performed as requested.

In a typical numerical-response scenario, here is how one would approach validating or deriving a probability like 0.8909:
- Identify the underlying model or prior information: determine whether the probability is derived from a Bernoulli/binomial setting, a Bayesian update, or another probabilistic framework.
- Check the given or assumed parameters: sample size, counts of success/failure, prior distributions, or likelihood functions relevant to the "previous exercise" referenced.
- Apply the appropriate calculation:
  - If it’s a simple empirical probability, compute successes divided by total trials.
  - If it’s a Bayesian posterior probability, combine prior and likelihood to obtain the posterior, then extract the predictive or posterior probability as required.
  - If it involves a predictive distribution for a new instance, integrate or evaluate the appropriate distribution at the target value.
- Verify units and rounding: ensure the result is presented with the requested precision (e.g., four decimal places) and that any rounding is consistent with the problem’s conventions.
- Consider edge cases: ensure the probability lies within [0,1] and that the calculation aligns with the question’s phrasing about a "new instance" from a prior exercise.

Without the answer options to critique or the explicit steps from the previous exercise, the reasoning cannot directly map to the given choices. If you supply the missing options or the context from the prior exercise, I can tailor a precise, option-by-option explanation and identify why the value 0.8909 fits (or adjust if it does not) along with explanations for any alternatives.

LH/LM Machine Learning 1b - Logistic Regression Hypothesis Set

What is the probability for the new instance in the previous exercise?

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