To solve the problem, we need to determine the probability of moving forward an even number of spaces based on the described game setup. Here's how we can approach it:
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Understanding the Move Choices:
- There are two outcomes for the pointer: moving forward or moving back.
- Presumably based on your description, the pointer could have a 50% chance of moving forward and a 50% chance of moving back. However, the details of the game (e.g., how these movements are determined) may affect these probabilities.
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Determining the Die Roll:
- The number cube (or die) has numbers from 1 to 6. The even numbers in this range are 2, 4, and 6.
- There are 3 even outcomes out of a total of 6 possible outcomes when rolling the die.
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Calculating Individual Probabilities:
- For moving forward:
- The probability of moving forward (if it is indeed 1/2 as inferred) multiplied by the probability of rolling an even number (3/6 = 1/2).
- So, \( P(\text{Forward}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \).
- For moving forward:
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Moving Back:
- The task specifically asks for the probability of moving forward an even number of spaces. The movement backwards does not impact this part of the calculation.
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Final Probability:
- Therefore, the final probability of moving forward an even number of spaces is \( \frac{1}{4} \).
So, the probability of Sam and Erica moving forward an even number of spaces is \( \frac{1}{4} \).
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