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
Steve
answered
0-2 represents a dog
3-4 represents a cat
5 represents other pet
6-9 represents no pet
then, sample groups of 5 digits as above, counting what percent contain two or more 0,1,2 digits
Explain Bot
answered
Step 1: Assign numbers to represent the outcomes.
- Assign numbers 00-39 to represent students with no pets.
- Assign numbers 40-59 to represent students with dogs.
- Assign numbers 60-69 to represent students with cats.
- Assign numbers 70-79 to represent students with other pets.
Step 2: Use the random-number table.
- Start at any location in the table and read the numbers from left to right, top to bottom.
- Ignore any numbers outside the range from 00 to 79.
- Continue reading until you have 5 different numbers.
Step 3: Count the number of times at least 2 students have a dog.
- If two or more of the numbers are in the range 40-49, it means at least 2 students have a dog.
Step 4: Repeat steps 2 and 3 multiple times.
- Repeat the process of using the random-number table and counting the number of times at least 2 students have a dog.
- Record the results each time.
Step 5: Calculate the experimental probability.
- Divide the total number of times at least 2 students have a dog by the total number of runs performed.
For part b, let's use the given random-number table and apply the steps to find the experimental probability:
Step 1: Assign numbers to represent the outcomes.
- Students with no pets: 00-39
- Students with dogs: 40-59
- Students with cats: 60-69
- Students with other pets: 70-79
Step 2: Use the random-number table.
- Starting at the first number in the table, read the numbers from left to right, top to bottom, until you have 5 valid numbers within the range 00-79:
- 65 9 2 6 3 1 4 5 9 3
Step 3: Count the number of times at least 2 students have a dog.
- From the sequence above, we have 2 numbers in the range 40-49, which means at least 2 students have a dog.
Step 4: Repeat the process multiple times.
- Perform steps 2 and 3 again using the next sequence of 5 numbers from the table.
Step 5: Calculate the experimental probability.
- Divide the total number of times at least 2 students have a dog by the total number of runs.
Remember, to get an accurate experimental probability, you need to repeat the process multiple times and then calculate the average.
