If a number is chosen at random from the integers 5 to 25 inclusive, find the probability that the number is
A.multiple of 5 or 3
B.even or prime number
C.less or greater than 18
A. To find the multiples of 5 or 3 from 5 to 25, we must find the multiples of 5 and the multiples of 3, and remove duplicates (15 and 20). The multiples of 5 are: 5, 10, 15, 20, and 25. The multiples of 3 are: 6, 9, 12, 15, 18, 21, and 24. So, the numbers that are multiples of 5 or 3 are: 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, making a total of 10 numbers. Therefore, the probability is:
P(multiple of 5 or 3) = 10/21
B. To find the even or prime numbers, we must identify which numbers are even and which ones are prime. The even numbers are: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. The prime numbers are: 5, 7, 11, 13, 17, 19, 23. So, the even or prime numbers are: 5, 6, 7, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, and 24, making a total of 16 numbers. Therefore, the probability is:
P(even or prime) = 16/21
C. To find the numbers that are less than or greater than 18, we just need to count them. The numbers less than or equal to 18 are: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18, making a total of 14 numbers. The numbers greater than 18 are: 19, 20, 21, 22, 23, and 24, making a total of 6 numbers. Therefore, the probability of choosing a number less than or greater than 18 is:
P(less or greater than 18) = 20/21
To find the probability, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
To do this, we'll work through each case separately:
A. Finding the probability of getting a number that is a multiple of 5 or 3:
1. Count the numbers that are multiples of 5: 5, 10, 15, 20, 25. There are 5 numbers.
2. Count the numbers that are multiples of 3: 6, 9, 12, 15, 18, 21, 24. There are 7 numbers.
3. Some numbers are counted twice (15), so we need to subtract 1 from the total count.
4. Add the two counts together: 5 + 7 - 1 = 11.
5. The total number of possible outcomes is 25 - 5 + 1 = 21 (from 5 to 25 inclusive).
So, the probability of getting a number that is a multiple of 5 or 3 is 11/21.
B. Finding the probability of getting a number that is even or a prime number:
1. Count the even numbers: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24. There are 10 numbers.
2. Count the prime numbers: 5, 7, 11, 13, 17, 19, 23. There are 7 numbers.
3. Some numbers are counted twice (10), so we need to subtract 1 from the total count.
4. Add the two counts together: 10 + 7 - 1 = 16.
5. The total number of possible outcomes is still 21.
So, the probability of getting a number that is even or a prime number is 16/21.
C. Finding the probability of getting a number that is less than or greater than 18:
1. Count the numbers less than 18: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. There are 13 numbers.
2. Count the numbers greater than 18: 19, 20, 21, 22, 23, 24, 25. There are 7 numbers.
3. Add the two counts together: 13 + 7 = 20.
4. The total number of possible outcomes is still 21.
So, the probability of getting a number that is less than or greater than 18 is 20/21.