If a number is chosen at random from 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
pr(multiple5) = pr(5)+pr(10)+pr(15)+pr(20)+pr(25)
= 5*pr(5)=5*1/21
pr even or prime=pr(even)+pr(prime)
= pr(6,8,10,12,14,16,18,20,22,24) + pr(5,7,11,13,17,19,23)
= 10/21+7/21=17/21
Pr(less or greater18)=1-pr(18)
= 1-1/21=20/21
Is it really correct
Thanks was helpful🥰
Amazing and kinda cool
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(a) Well, to find the probability of getting a number that is a multiple of 5 or 3, we need to first determine how many numbers in the range from 5 to 25 inclusive satisfy this condition.
Numbers that are multiples of 5: 5, 10, 15, 20, 25
Numbers that are multiples of 3: 6, 9, 12, 15, 18, 21, 24
Let's combine these lists and remove any duplicates: 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25.
There are 11 numbers in total that are multiples of 5 or 3. Since we have a total of 21 numbers in the given range, the probability is 11/21.
(b) Now, let's determine the probability of getting a number that is even or a prime number.
Even numbers in the range from 5 to 25 inclusive: 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.
Prime numbers in the range from 5 to 25 inclusive: 5, 7, 11, 13, 17, 19, 23.
Again, we'll combine these lists and remove any duplicates: 5, 6, 7, 8, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24.
There are 17 numbers in total that are either even or prime. The probability is therefore 17/21.
(c) Lastly, we need to determine the probability of getting a number that is either less than or greater than 18.
Numbers less than 18 in the range from 5 to 25 inclusive: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17.
Numbers greater than 18 in the range from 5 to 25 inclusive: 19, 20, 21, 22, 23, 24, 25.
We have a total of 20 numbers that are either less than or greater than 18. The probability is 20/21.
Remember, these are just mathematical probabilities. In reality, numbers can sometimes be a little unpredictable - just like my jokes! But hey, that's why we calculate probabilities, to understand the likelihood of certain outcomes.
To find the probability in each case, we need to determine the favorable outcomes and the total number of outcomes.
(a) Probability that the number is a multiple of 5 or 3:
To find the favorable outcomes, we need to count the numbers between 5 and 25 (inclusive) that are multiples of 5 or 3. These numbers are: 5, 6, 9, 10, 12, 15, 18, 20, and 24.
Total number of outcomes = 25 - 5 + 1 = 21 (as there are 21 numbers between 5 and 25 inclusive).
Therefore, the probability of choosing a number that is a multiple of 5 or 3 is 9/21 or simplified as 3/7.
(b) Probability that the number is even or a prime number:
To find the favorable outcomes, we need to count the numbers between 5 and 25 (inclusive) that are even or prime. Even numbers between 5 and 25 are: 6, 8, 10, 12, 14, 16, 18, 20, 22, and 24. Prime numbers between 5 and 25 are: 5, 7, 11, 13, 17, 19, and 23.
Total number of outcomes is still 21.
Therefore, the probability of choosing a number that is even or a prime number is (10 + 7)/21 = 17/21.
(c) Probability that the number is less than or greater than 18:
To find the favorable outcomes, we need to count the numbers between 5 and 25 (inclusive) that are less than or greater than 18. Numbers less than 18 are: 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17. Numbers greater than 18 are: 19, 20, 21, 22, 23, 24, and 25.
Total number of outcomes is still 21.
Therefore, the probability of choosing a number that is less than or greater than 18 is (13 + 7)/21 = 20/21.