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Sagot :
To determine the probability that the first day of winter will be a snowy Monday, let's consider the probabilities involved:
1. Probability of Snow on the First Day of Winter: Given as [tex]\(\frac{1}{6}\)[/tex], which equals approximately [tex]\(0.16666666666666666\)[/tex].
2. Probability that the First Day of Winter is a Monday: Since there are 7 days in a week, the probability that any given day (including the first day of winter) is Monday is [tex]\(\frac{1}{7}\)[/tex], which equals approximately [tex]\(0.14285714285714285\)[/tex].
3. Combined Probability that the First Day of Winter is Both Snowy and a Monday:
To find the probability of both events happening simultaneously, multiply their individual probabilities:
[tex]\[ \frac{1}{6} \times \frac{1}{7} = \frac{1}{42} \][/tex]
[tex]\[ \frac{1}{42} \approx 0.023809523809523808 \][/tex]
Now, to simulate this scenario using a number cube and a spinner, we need to look for a method that mirrors these probabilities.
Simulation Method:
1. Roll a number cube (which has 6 faces) to represent the probability of snow falling on the first day of winter.
2. Spin a spinner divided into 7 equal parts to represent the probability that the first day of winter is a Monday.
The appropriate method in the tables provided is:
Method: Roll and spin 50 times. Count the number of times you ... Roll a 1 or 6 AND land on red.
This method is closest because:
- Rolling a 1 or 6 on a 6-faced cube happens [tex]\(\frac{2}{6}\)[/tex] or [tex]\(\frac{1}{3}\)[/tex] of the time.
- Landing on a specific color (e.g., red) on a 7-part spinner happens [tex]\(\frac{1}{7}\)[/tex] of the time.
The multiplication of these two probabilities [tex]\(\frac{1}{3} \times \frac{1}{7} = \frac{1}{21}\)[/tex], which is not exact, but only \\
off by a factor due to limited choices of configurations given in the question. For exactness:
Rolling a 1 on the cube representing exact 1/6 and the spinner landing any specific part 1/7 would give exact match for the required computation of 1/42.
Thus, even though the optical method given it provided gets close statistical example simulates closely to probabilities matching to (snow 1/6 times and picking 1/7 for Monday) to get snowy Monday. That makes using ‘Roll and spin 50 times, count the number of Roll 1 or 6 times and land on a red color’ best fit for the simulation purpose provided by your choice methods structured example.
1. Probability of Snow on the First Day of Winter: Given as [tex]\(\frac{1}{6}\)[/tex], which equals approximately [tex]\(0.16666666666666666\)[/tex].
2. Probability that the First Day of Winter is a Monday: Since there are 7 days in a week, the probability that any given day (including the first day of winter) is Monday is [tex]\(\frac{1}{7}\)[/tex], which equals approximately [tex]\(0.14285714285714285\)[/tex].
3. Combined Probability that the First Day of Winter is Both Snowy and a Monday:
To find the probability of both events happening simultaneously, multiply their individual probabilities:
[tex]\[ \frac{1}{6} \times \frac{1}{7} = \frac{1}{42} \][/tex]
[tex]\[ \frac{1}{42} \approx 0.023809523809523808 \][/tex]
Now, to simulate this scenario using a number cube and a spinner, we need to look for a method that mirrors these probabilities.
Simulation Method:
1. Roll a number cube (which has 6 faces) to represent the probability of snow falling on the first day of winter.
2. Spin a spinner divided into 7 equal parts to represent the probability that the first day of winter is a Monday.
The appropriate method in the tables provided is:
Method: Roll and spin 50 times. Count the number of times you ... Roll a 1 or 6 AND land on red.
This method is closest because:
- Rolling a 1 or 6 on a 6-faced cube happens [tex]\(\frac{2}{6}\)[/tex] or [tex]\(\frac{1}{3}\)[/tex] of the time.
- Landing on a specific color (e.g., red) on a 7-part spinner happens [tex]\(\frac{1}{7}\)[/tex] of the time.
The multiplication of these two probabilities [tex]\(\frac{1}{3} \times \frac{1}{7} = \frac{1}{21}\)[/tex], which is not exact, but only \\
off by a factor due to limited choices of configurations given in the question. For exactness:
Rolling a 1 on the cube representing exact 1/6 and the spinner landing any specific part 1/7 would give exact match for the required computation of 1/42.
Thus, even though the optical method given it provided gets close statistical example simulates closely to probabilities matching to (snow 1/6 times and picking 1/7 for Monday) to get snowy Monday. That makes using ‘Roll and spin 50 times, count the number of Roll 1 or 6 times and land on a red color’ best fit for the simulation purpose provided by your choice methods structured example.
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