Question
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 marbles is P(r)= 1/
The sample space change.
each event within the sample space change. The probability of each event change.
the new probability of drawing a red marbles is P(r)= 1/
Answers
GPT-4o mini
To analyze the effects of adding 10 yellow marbles to the jar, we will consider the three aspects you mentioned: the sample space, the events within the sample space, and the probabilities of those events.
1. **The Sample Space**:
- If Mr. Campbell adds 10 yellow marbles to the jar, the total number of marbles in the jar increases. This does change the sample space, as the sample space, which is the set of all possible outcomes (in this case, the different colored marbles), now includes more yellow marbles.
2. **Each Event Within the Sample Space**:
- The events (e.g., drawing a red marble, yellow marble, etc.) depend on the composition of the marbles in the jar. Since you added yellow marbles, the events related to drawing a yellow marble will increase in probability. Therefore, this aspect does also change.
3. **The Probability of Each Event**:
- The probability of each event will change because the total number of marbles in the jar (the denominator) has increased. For example, if the previous composition was such that there were \( r \) red marbles, and now with the increased total due to the 10 yellow marbles, the probability of drawing a red marble (P(r)) is calculated as the number of red marbles divided by the total number of marbles. Thus, the probability of drawing a red marble will change.
Now, regarding the probability of drawing a red marble:
Let’s assume the initial number of red marbles is \( r \), and the initial number of yellow marbles is \( y \). After adding the 10 yellow marbles, the new total number of yellow marbles is \( y + 10 \), and the total number of marbles in the jar becomes:
\[
\text{Total marbles} = r + (y + 10) = r + y + 10
\]
Thus, the new probability of drawing a red marble can be expressed as:
\[
P(r) = \frac{r}{r + y + 10}
\]
If you know the values for \( r \) and \( y \), you can substitute them into this formula to find the new probability \( P(r) \).
1. **The Sample Space**:
- If Mr. Campbell adds 10 yellow marbles to the jar, the total number of marbles in the jar increases. This does change the sample space, as the sample space, which is the set of all possible outcomes (in this case, the different colored marbles), now includes more yellow marbles.
2. **Each Event Within the Sample Space**:
- The events (e.g., drawing a red marble, yellow marble, etc.) depend on the composition of the marbles in the jar. Since you added yellow marbles, the events related to drawing a yellow marble will increase in probability. Therefore, this aspect does also change.
3. **The Probability of Each Event**:
- The probability of each event will change because the total number of marbles in the jar (the denominator) has increased. For example, if the previous composition was such that there were \( r \) red marbles, and now with the increased total due to the 10 yellow marbles, the probability of drawing a red marble (P(r)) is calculated as the number of red marbles divided by the total number of marbles. Thus, the probability of drawing a red marble will change.
Now, regarding the probability of drawing a red marble:
Let’s assume the initial number of red marbles is \( r \), and the initial number of yellow marbles is \( y \). After adding the 10 yellow marbles, the new total number of yellow marbles is \( y + 10 \), and the total number of marbles in the jar becomes:
\[
\text{Total marbles} = r + (y + 10) = r + y + 10
\]
Thus, the new probability of drawing a red marble can be expressed as:
\[
P(r) = \frac{r}{r + y + 10}
\]
If you know the values for \( r \) and \( y \), you can substitute them into this formula to find the new probability \( P(r) \).