Asked by jojo
Mr. Campbell decides that too many students are getting a pass on homework. He adds 10 yellow marbles to the jar. Tell whether each part of the probability model does or does not change.
The sample space change. Each event within the sample space change. The probability of each event change.
The new probability of drawing a red marble is 𝘗(𝖱)=𝟣.
Convince Me!
How does a probability model help you predict how likely an event is to occur?
All Answers 1
Answered by
GPT-5 mini
AI
Short answers (with why):
- The sample space — changes.
Why: the set of possible individual outcomes grows (you've added 10 distinct marbles), and if yellow was not previously present then the list of possible colors also increases. Either way the collection of outcomes and their relative counts change.
- Each event (as a description, e.g. "draw a red marble") — does not change.
Why: the events themselves (the descriptions/subsets of outcomes like "red", "blue", "yellow") remain the same kinds of questions you can ask. What does change is how many outcomes in each event.
- The probability of each event — changes (in general).
Why: probability = (number of favorable marbles)/(total number of marbles). Adding 10 yellow marbles increases the denominator (and increases the count for the yellow event), so most event probabilities change. For example, the new probability of drawing a red marble is
P(R) = (# red) / (total marbles + 10),
which is smaller than before (unless # red was 0, in which case it stays 0). So P(R) = 1 is false unless every marble in the jar is red and there are no non-red marbles — adding yellow marbles makes P(R) strictly less than 1.
Convince me: How a probability model helps predict likelihood
- A probability model lists the sample space and assigns probabilities to each outcome. These probabilities (numbers between 0 and 1) tell you the expected long-run proportion of times an event will occur if you repeat the random process many times.
- Practically, it lets you compute probabilities (e.g. P(red) = #red/total) so you can compare which events are more or less likely, predict expected counts, and make decisions based on those chances.
- The sample space — changes.
Why: the set of possible individual outcomes grows (you've added 10 distinct marbles), and if yellow was not previously present then the list of possible colors also increases. Either way the collection of outcomes and their relative counts change.
- Each event (as a description, e.g. "draw a red marble") — does not change.
Why: the events themselves (the descriptions/subsets of outcomes like "red", "blue", "yellow") remain the same kinds of questions you can ask. What does change is how many outcomes in each event.
- The probability of each event — changes (in general).
Why: probability = (number of favorable marbles)/(total number of marbles). Adding 10 yellow marbles increases the denominator (and increases the count for the yellow event), so most event probabilities change. For example, the new probability of drawing a red marble is
P(R) = (# red) / (total marbles + 10),
which is smaller than before (unless # red was 0, in which case it stays 0). So P(R) = 1 is false unless every marble in the jar is red and there are no non-red marbles — adding yellow marbles makes P(R) strictly less than 1.
Convince me: How a probability model helps predict likelihood
- A probability model lists the sample space and assigns probabilities to each outcome. These probabilities (numbers between 0 and 1) tell you the expected long-run proportion of times an event will occur if you repeat the random process many times.
- Practically, it lets you compute probabilities (e.g. P(red) = #red/total) so you can compare which events are more or less likely, predict expected counts, and make decisions based on those chances.
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