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 numbers
c) less or greater than 18

Solution

5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Total outcome= 21
a) p(multiple of 5 & 3)= 5/21+7/21= 5+7/21= 12/21= 4/7ans
b) p( Even or prime number)= 10/21+7/21= 10+7/21= 17/21ans
c) p(less or greater than 18)= 13/21+7/21= 13+7/21= 20/21ans

HOW DID YOU GET THE DIVISIBLE NUMBER BY 5 OR 3

5 6 7 8 9 10 11 12 13 14 15 16 17 18

19 20 21 22 23 24 25

You have 21 numbers

Which of these numbers are divisible by 5 or 3

5,6,12,15,18,20,21,24,25

9/21 or a decimal if your teacher requires that format.

b) count up the even numbers and the prime numbers. Prime numbers are only divisible by 1 and itself.

Put this answer over 21.

c) all the numbers except 18. right? count them and divide by 21.

a) Ah, the probability game! Alright, let's see. The total numbers we have in the range from 5 to 25 are 21. Now let's count the multiples of 5: 5, 10, 15, 20, and 25. That's five numbers! And the multiples of 3 are: 6, 9, 12, 15, 18, 21, and 24. That's seven numbers! But wait, two of these numbers are overlapping, namely 15 and 25. So if we subtract them, we get 10 different numbers. Therefore, the probability of choosing a multiple of 5 or 3 is 10 out of 21, which is approximately 0.476. That's like having a 47.6% chance of winning a clown's heart!

b) Ah, we're onto the next probability challenge! Okay, let's break it down like this. Even numbers within the range are: 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24. That's 10 numbers! As for prime numbers, let's see... 5, 7, 11, 13, 17, 19, and 23. Hmm, seven numbers! But wait, we have a teeny-tiny overlap again with the number 18, which is both even and prime (naughty number). So subtracting 18, we get 16 different numbers. Therefore, the probability of choosing an even or prime number is 16 out of 21, which is roughly 0.762. You've got a 76.2% chance, which is higher than the chance of me fitting into my tiny clown car comfortably!

c) Let's dive into another probability adventure! We need to find the probability of choosing a number that is either less than 18 or greater than 18. Well, considering that there are 21 numbers in total, and since 18 is included, we can divide the range into two parts: numbers less than 18 and numbers greater than 18. There are 12 numbers less than 18 (5 to 17), and there are 8 numbers greater than 18 (19 to 25). Now add those two together, and we get 12 + 8 = 20. So out of the 21 numbers, there are 20 that are either less than or greater than 18. Therefore, the probability of choosing a number less than or greater than 18 is 20 out of 21, which is approximately 0.952. You've got an astonishing 95.2% chance of not being right on the edge of 18 - how thrilling!

To find the probability in each case, we first need to determine the total number of possible outcomes and the number of favorable outcomes.

a) To find the probability of choosing a number that is a multiple of 5 or 3, we need to count the numbers between 5 and 25 (inclusive) that are divisible by 5 or 3.

Divisible by 5: The numbers between 5 and 25 (inclusive) that are divisible by 5 are 5, 10, 15, 20, and 25.

Divisible by 3: The numbers between 5 and 25 (inclusive) that are divisible by 3 are 6, 9, 12, 15, 18, 21, and 24.

Note that 15 appears in both lists since it is divisible by both 3 and 5.

Therefore, the total number of favorable outcomes is 9 (5, 10, 15, 20, 25, 6, 9, 12, and 24) and the total number of possible outcomes is 21 (from 5 to 25).

Thus, the probability of choosing a number that is a multiple of 5 or 3 is 9/21, which simplifies to 3/7.

b) To find the probability of choosing a number that is even or prime, we need to count the numbers between 5 and 25 (inclusive) that are even or prime.

Even numbers: The even numbers between 5 and 25 (inclusive) are 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24.

Prime numbers: The prime numbers between 5 and 25 (inclusive) are 5, 7, 11, 13, 17, 19, and 23.

Therefore, the total number of favorable outcomes is 17 (10 even numbers + 7 prime numbers) and the total number of possible outcomes is 21 (from 5 to 25).

Thus, the probability of choosing a number that is even or prime is 17/21.

c) To find the probability of choosing a number that is less than or greater than 18, we need to count the numbers between 5 and 25 (inclusive) that are less than 18 or greater than 18.

Numbers less than 18: The numbers between 5 and 25 (inclusive) that are less than 18 are 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17.

Numbers greater than 18: The numbers between 5 and 25 (inclusive) that are greater than 18 are 19, 20, 21, 22, 23, 24, and 25.

Therefore, the total number of favorable outcomes is 20 (13 numbers less than 18 + 7 numbers greater than 18) and the total number of possible outcomes is 21 (from 5 to 25).

Thus, the probability of choosing a number that is less than or greater than 18 is 20/21.