the number 1 to 20 are written on pieces of paper and put in the box. if a piece of paper is picked at random, what is the probability of picking a paper with: an odd number, a prime number, a multiple of 3 and a square numbe
20 total.
How many primes? 2,3,5,7,11,13,17,19 = 8 so P(prime)=8/20
work the others the same way.
To find the probabilities of picking papers with specific properties from the box of numbers 1 to 20, we need to calculate the ratios of favorable outcomes to all possible outcomes.
1. Probability of picking an odd number:
In the range from 1 to 20, there are 10 odd numbers (1, 3, 5, 7, 9, 11, 13, 15, 17, and 19) and a total of 20 numbers. Thus, the probability of picking an odd number is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 10 / 20
Probability = 1/2 or 0.5
2. Probability of picking a prime number:
Among the numbers from 1 to 20, the prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19. There are a total of 8 prime numbers in this range. So, the probability of picking a prime number is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 8 / 20
Probability = 2/5 or 0.4
3. Probability of picking a multiple of 3:
From the numbers 1 to 20, the multiples of 3 are 3, 6, 9, 12, 15, and 18. There are a total of 6 multiples of 3 in this range. Therefore, the probability of picking a multiple of 3 is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 6 / 20
Probability = 3/10 or 0.3
4. Probability of picking a square number:
Among the numbers from 1 to 20, the square numbers are 1, 4, 9, and 16. There are a total of 4 square numbers in this range. Hence, the probability of picking a square number is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 4 / 20
Probability = 1/5 or 0.2
To summarize:
- The probability of picking an odd number is 0.5 or 50%.
- The probability of picking a prime number is 0.4 or 40%.
- The probability of picking a multiple of 3 is 0.3 or 30%.
- The probability of picking a square number is 0.2 or 20%.