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A coin is flipped. Then a number cube with sides labeled 1 through 6 is rolled.
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Event A: The coin toss is heads.
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& \multirow[b]{2}{}{0}
& \multirow[b]{2}{}{0} \\
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& \begin{tabular}{l}
Event B: The number cube roll is a 1.
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A paper clip is randomly selected from a container with green clips and white clips and returned to the container. The paper clips are mixed. Then another random selection is made.
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& \begin{tabular}{l}
Event A: The first selection is a white paper clip.
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Event B: The second selection is a green paper clip.
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A box contains assorted chocolates. Some chocolates contain only nuts and the others contain only cherries. A chocolate is randomly selected and eaten. Then another random selection is made from the remaining chocolates.
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Event A: The first selection contains nuts.
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& \multirow[b]{2}{}{0}
& \multirow[b]{2}{*}{0} \\
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& \begin{tabular}{l}
Event B: The second selection contains cherries.
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Answer :

GinnyAnswer
Sure, let's look at the problem step-by-step to understand and solve it in detail.

### Scenario 1: Flipping a Coin and Rolling a Number Cube

1. Event A: The coin toss is heads.
2. Event B: The number cube roll is a 1.

For Event A:
- When you flip a coin, there are two possible outcomes: heads or tails.
- The probability of getting heads (Event A) is [tex]\(\frac{1}{2}\)[/tex] or [tex]\(0.5\)[/tex].

For Event B:
- When you roll a number cube (a six-sided die), there are six possible outcomes: 1, 2, 3, 4, 5, or 6.
- The probability of rolling a 1 (Event B) is [tex]\(\frac{1}{6}\)[/tex] or approximately [tex]\(0.16666666666666666\)[/tex].

### Scenario 2: Selecting Paper Clips

1. Event A: The first selection is a white paper clip.
2. Event B: The second selection is a green paper clip.

For these events, we need to know the composition of the paper clips in the container (e.g., the number of white and green paper clips). Without this information, the probabilities for Event A and Event B are unknown.

### Scenario 3: Selecting Chocolates with Nuts and Cherries

1. Event A: The first selection contains nuts.
2. Event B: The second selection contains cherries.

For these events, we need to know the initial number of chocolates with nuts and cherries, and how many remain after the first chocolate is selected. Without this information, the probabilities for Event A and Event B are unknown.

### Summary

Given this information, the probabilities are:
1. For the event of flipping a coin and then rolling a die:
- Probability of getting heads (Event A): [tex]\(0.5\)[/tex]
- Probability of rolling a 1 on a die (Event B): [tex]\(0.16666666666666666 \approx \frac{1}{6}\)[/tex]

2. For the event of randomly selecting a white paper clip then a green one:
- Probability of the first selection being a white paper clip (Event A): Unknown
- Probability of the second selection being a green paper clip (Event B): Unknown

3. For the event of selecting chocolates (first with nuts, then with cherries):
- Probability of the first selection containing nuts (Event A): Unknown
- Probability of the second selection containing cherries (Event B): Unknown

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