I need help with this really bad.
At West Middle School, 30% of students have a dog, 20% of students have a cat, 10% of students have another kind of pet, and 40% of students have no pets.
a) Explain how you can use a random-number table to find the experimental probability that in a group of 5 students, at least 2 will have a dog.
b) Use your model from part a and the table below to find the experimental probability that in a group of 5 students, at least 2 will have a dog.
65926 31459 31986 65809 80462
27387 39075 46738 21986 59837
91384 10987 26491 68498 98796
32596 26448 31235 63256 53121
a) To use a random-number table to find the experimental probability, follow these steps:
1. Assign each outcome in the sample space a unique number.
- In this case, we have four outcomes: having a dog, having a cat, having another kind of pet, and having no pets.
- Assign them numbers 1, 2, 3, and 4, respectively.
2. Determine the number of digits in the random-number table.
- In this case, each number in the table has 5 digits.
3. Starting from the first number in the random-number table, use each digit to select an outcome from the sample space.
- If the digit is 1 or 2, the student has a dog.
- If the digit is 3, the student has a cat.
- If the digit is 4 or 5, the student has another kind of pet.
- If the digit is 6, 7, 8, or 9, the student has no pets.
4. Repeat the process for as many students as required.
- In this case, we need to select 5 students, so repeat the process 5 times.
5. Count the number of outcomes that satisfy the condition of interest.
- In this case, we are interested in the number of students who have at least 2 dogs.
6. Calculate the experimental probability by dividing the number of outcomes that satisfy the condition by the total number of trials.
- The experimental probability is the ratio of the number of successful outcomes to the total number of trials.
b) Using the random-number table provided, let's follow the steps outlined in part a:
1. Assign each outcome a unique number:
- Having a dog: outcome 1
- Having a cat: outcome 2
- Having another kind of pet: outcome 3
- Having no pets: outcome 4
2. Determine the number of digits in the random-number table:
- Each number has 5 digits.
3. Starting from the first number in the table, use each digit to select an outcome:
- First number: 65926
- First digit: 6 – student has no pets (outcome 4)
- Second digit: 5 – student has another kind of pet (outcome 3)
- Third digit: 9 – student has no pets (outcome 4)
- Fourth digit: 2 – student has a cat (outcome 2)
- Fifth digit: 6 – student has no pets (outcome 4)
- Second number: 31459
- First digit: 3 – student has a cat (outcome 2)
- Second digit: 1 – student has a dog (outcome 1)
- Third digit: 4 – student has another kind of pet (outcome 3)
- Fourth digit: 5 – student has another kind of pet (outcome 3)
- Fifth digit: 9 – student has no pets (outcome 4)
- Continue this process for the remaining numbers in the table.
4. Count the number of outcomes that satisfy the condition:
- Since we are interested in the probability of at least 2 students having a dog, we need to look for outcomes where there are 2 or more occurrences of outcome 1 (having a dog).
5. Calculate the experimental probability:
- Count the number of outcomes where there are at least 2 "outcome 1" occurrences and divide it by the total number of trials (5 in this case).
By following these steps, you can determine the experimental probability that in a group of 5 students, at least 2 will have a dog using the provided random-number table.