Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
Sure, let's find the probabilities step by step.
### Prime Numbers between 1 and 25
First, let's list out all the prime numbers between 1 and 25. They are:
[tex]\[ 2, 3, 5, 7, 11, 13, 17, 19, 23 \][/tex]
There are 9 prime numbers in total.
### i. Probability of Getting a One-Digit Number
The one-digit prime numbers are:
[tex]\[ 2, 3, 5, 7 \][/tex]
There are 4 one-digit prime numbers. Therefore, the probability [tex]\(P\)[/tex] of drawing a one-digit prime number is:
[tex]\[ P(\text{one-digit number}) = \frac{\text{Number of one-digit primes}}{\text{Total number of primes}} = \frac{4}{9} \approx 0.4444444444444444 \][/tex]
### ii. Probability of Getting an Odd Number
The odd prime numbers are:
[tex]\[ 3, 5, 7, 11, 13, 17, 19, 23 \][/tex]
There are 8 odd prime numbers. Therefore, the probability [tex]\(P\)[/tex] of drawing an odd prime number is:
[tex]\[ P(\text{odd number}) = \frac{\text{Number of odd primes}}{\text{Total number of primes}} = \frac{8}{9} \approx 0.8888888888888888 \][/tex]
### iii. Probability of Getting an Even Number
The even prime number is:
[tex]\[ 2 \][/tex]
There is 1 even prime number. Therefore, the probability [tex]\(P\)[/tex] of drawing an even prime number is:
[tex]\[ P(\text{even number}) = \frac{\text{Number of even primes}}{\text{Total number of primes}} = \frac{1}{9} \approx 0.1111111111111111 \][/tex]
### iv. Probability of Getting a Number Greater than 11
The prime numbers greater than 11 are:
[tex]\[ 13, 17, 19, 23 \][/tex]
There are 4 prime numbers greater than 11. Therefore, the probability [tex]\(P\)[/tex] of drawing a prime number greater than 11 is:
[tex]\[ P(\text{greater than 11}) = \frac{\text{Number of primes greater than 11}}{\text{Total number of primes}} = \frac{4}{9} \approx 0.4444444444444444 \][/tex]
### Summary of Results
- Probability of getting a one-digit number: [tex]\( \approx 0.4444444444444444 \)[/tex]
- Probability of getting an odd number: [tex]\( \approx 0.8888888888888888 \)[/tex]
- Probability of getting an even number: [tex]\( \approx 0.1111111111111111 \)[/tex]
- Probability of getting a number greater than 11: [tex]\( \approx 0.4444444444444444 \)[/tex]
These probabilities are based on the total of 9 prime numbers between 1 and 25.
### Prime Numbers between 1 and 25
First, let's list out all the prime numbers between 1 and 25. They are:
[tex]\[ 2, 3, 5, 7, 11, 13, 17, 19, 23 \][/tex]
There are 9 prime numbers in total.
### i. Probability of Getting a One-Digit Number
The one-digit prime numbers are:
[tex]\[ 2, 3, 5, 7 \][/tex]
There are 4 one-digit prime numbers. Therefore, the probability [tex]\(P\)[/tex] of drawing a one-digit prime number is:
[tex]\[ P(\text{one-digit number}) = \frac{\text{Number of one-digit primes}}{\text{Total number of primes}} = \frac{4}{9} \approx 0.4444444444444444 \][/tex]
### ii. Probability of Getting an Odd Number
The odd prime numbers are:
[tex]\[ 3, 5, 7, 11, 13, 17, 19, 23 \][/tex]
There are 8 odd prime numbers. Therefore, the probability [tex]\(P\)[/tex] of drawing an odd prime number is:
[tex]\[ P(\text{odd number}) = \frac{\text{Number of odd primes}}{\text{Total number of primes}} = \frac{8}{9} \approx 0.8888888888888888 \][/tex]
### iii. Probability of Getting an Even Number
The even prime number is:
[tex]\[ 2 \][/tex]
There is 1 even prime number. Therefore, the probability [tex]\(P\)[/tex] of drawing an even prime number is:
[tex]\[ P(\text{even number}) = \frac{\text{Number of even primes}}{\text{Total number of primes}} = \frac{1}{9} \approx 0.1111111111111111 \][/tex]
### iv. Probability of Getting a Number Greater than 11
The prime numbers greater than 11 are:
[tex]\[ 13, 17, 19, 23 \][/tex]
There are 4 prime numbers greater than 11. Therefore, the probability [tex]\(P\)[/tex] of drawing a prime number greater than 11 is:
[tex]\[ P(\text{greater than 11}) = \frac{\text{Number of primes greater than 11}}{\text{Total number of primes}} = \frac{4}{9} \approx 0.4444444444444444 \][/tex]
### Summary of Results
- Probability of getting a one-digit number: [tex]\( \approx 0.4444444444444444 \)[/tex]
- Probability of getting an odd number: [tex]\( \approx 0.8888888888888888 \)[/tex]
- Probability of getting an even number: [tex]\( \approx 0.1111111111111111 \)[/tex]
- Probability of getting a number greater than 11: [tex]\( \approx 0.4444444444444444 \)[/tex]
These probabilities are based on the total of 9 prime numbers between 1 and 25.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.
