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 number
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To determine the probability of picking a paper with certain characteristics, we need to calculate the ratio of the number of papers with those characteristics to the total number of papers in the box.
1. Odd number:
Out of the numbers from 1 to 20, half of them are odd (1, 3, 5, ..., 19). So, there are 10 odd numbers.
2. Prime number:
To find the prime numbers between 1 and 20, we can use a method called the sieve of Eratosthenes. Starting from 2, we mark all the multiples of each prime number as non-prime. After applying this method, we find that the prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19. So, there are 8 prime numbers.
3. Multiple of 3:
To find the multiples of 3 between 1 and 20, we list them as follows: 3, 6, 9, 12, 15, 18. So, there are 6 multiples of 3.
4. Square number:
The squares between 1 and 20 are 1, 4, 9, 16. So, there are 4 square numbers.
Now that we have determined the number of papers with each characteristic, we can calculate the probabilities:
1. Probability of picking an odd number:
Probability = (Number of odd numbers) / (Total number of papers) = 10 / 20 = 1/2 = 0.5
2. Probability of picking a prime number:
Probability = (Number of prime numbers) / (Total number of papers) = 8 / 20 = 2/5 = 0.4
3. Probability of picking a multiple of 3:
Probability = (Number of multiples of 3) / (Total number of papers) = 6 / 20 = 3/10 = 0.3
4. Probability of picking a square number:
Probability = (Number of square numbers) / (Total number of papers) = 4 / 20 = 1/5 = 0.2
So, the probability of picking a paper with an odd number is 0.5, with a prime number is 0.4, with a multiple of 3 is 0.3, and with a square number is 0.2.