Discover the answers you need at Westonci.ca, a dynamic Q&A platform where knowledge is shared freely by a community of experts. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To simulate the probability of a snowy Friday, we need to consider two independent probabilities: the probability of it snowing on the first day of winter and the probability that the first day of winter is a Friday.
Step 1: Understand the given probabilities
1. The probability that it will snow on the first day of winter is given as [tex]\(\frac{2}{3}\)[/tex], which translates to approximately 0.6667 or 66.67%.
2. The probability that any given day is a Friday, given that there are 7 days in a week, is [tex]\(\frac{1}{7}\)[/tex], which is approximately 0.1429 or 14.29%.
Step 2: Simulate the probabilities
### Available Methods for Simulation
- Method 1: Roll a die 8 times and count the number of times you roll a number greater than 2.
- Method 2: Pick a marble and replace it 100 times, counting the number of times you pick a yellow marble.
- Method 3: Roll a die, pick and replace a marble 100 times, and count the number of times you roll greater than 2 and pick a green marble.
- Method 4: Roll a die 8 times and count the number of times you roll a 2 and pick and replace a yellow marble.
- Method 5: Roll a die, pick and replace a marble 100 times, and count the number of times you roll a 5 and pick a green marble.
### Selecting the Appropriate Simulation
From these methods, we need to find the one that accurately simulates choosing a year at random and checking if the first day of winter will be both snowy and a Friday.
We need both probabilities to be correctly represented:
- Rolling a die to simulate the snow probability.
- Picking a marble from a hat to simulate the day being a Friday.
Correct Method:
- Roll a die, pick and replace a marble 100 times, and count the number of times you roll ≥ 5 and pick a green marble.
This correctly aligns as rolling ≥ 5 simulates the [tex]\(\frac{2}{3}\)[/tex] probability of snow (since rolling 5 or 6 out of 6 choices approximates to [tex]\(\frac{2}{3}\)[/tex]), and picking one specific color from 7 (green marble) simulates the [tex]\(\frac{1}{7}\)[/tex] probability of the day being a Friday.
Step 3: Finding the combined probability
From our given results:
1. Snow probability = 0.6667
2. Friday probability = 0.1429
To find the probability of both happening (snowy Friday):
[tex]\[ P(\text{Snowy Friday}) = \text{Snow probability} \times \text{Friday probability} \][/tex]
[tex]\[ P(\text{Snowy Friday}) = 0.6667 \times 0.1429 \approx 0.0952 \][/tex]
This result implies that there is approximately a 9.52% chance that the first day of winter will be a snowy Friday when choosing a year at random.
Step 1: Understand the given probabilities
1. The probability that it will snow on the first day of winter is given as [tex]\(\frac{2}{3}\)[/tex], which translates to approximately 0.6667 or 66.67%.
2. The probability that any given day is a Friday, given that there are 7 days in a week, is [tex]\(\frac{1}{7}\)[/tex], which is approximately 0.1429 or 14.29%.
Step 2: Simulate the probabilities
### Available Methods for Simulation
- Method 1: Roll a die 8 times and count the number of times you roll a number greater than 2.
- Method 2: Pick a marble and replace it 100 times, counting the number of times you pick a yellow marble.
- Method 3: Roll a die, pick and replace a marble 100 times, and count the number of times you roll greater than 2 and pick a green marble.
- Method 4: Roll a die 8 times and count the number of times you roll a 2 and pick and replace a yellow marble.
- Method 5: Roll a die, pick and replace a marble 100 times, and count the number of times you roll a 5 and pick a green marble.
### Selecting the Appropriate Simulation
From these methods, we need to find the one that accurately simulates choosing a year at random and checking if the first day of winter will be both snowy and a Friday.
We need both probabilities to be correctly represented:
- Rolling a die to simulate the snow probability.
- Picking a marble from a hat to simulate the day being a Friday.
Correct Method:
- Roll a die, pick and replace a marble 100 times, and count the number of times you roll ≥ 5 and pick a green marble.
This correctly aligns as rolling ≥ 5 simulates the [tex]\(\frac{2}{3}\)[/tex] probability of snow (since rolling 5 or 6 out of 6 choices approximates to [tex]\(\frac{2}{3}\)[/tex]), and picking one specific color from 7 (green marble) simulates the [tex]\(\frac{1}{7}\)[/tex] probability of the day being a Friday.
Step 3: Finding the combined probability
From our given results:
1. Snow probability = 0.6667
2. Friday probability = 0.1429
To find the probability of both happening (snowy Friday):
[tex]\[ P(\text{Snowy Friday}) = \text{Snow probability} \times \text{Friday probability} \][/tex]
[tex]\[ P(\text{Snowy Friday}) = 0.6667 \times 0.1429 \approx 0.0952 \][/tex]
This result implies that there is approximately a 9.52% chance that the first day of winter will be a snowy Friday when choosing a year at random.
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
