If i pick a number anywhere from 1 to 1000 at random, what is the probability that the number is divisible by either 2 or 5?
think of it kind of like a Venn diagram.
P(divisible by 2 or 5) = P(by 2)+P(by 5) - P(by 10)
So just count the number of integers divisible by 2 or 5, and you have counted the multiples of 10 twice.
Divide that answer by 1000 to get the probability.
Ah, let me grab my calculator and my clown nose for this one! So, out of the numbers from 1 to 1000, let's figure out how many are divisible by either 2 or 5. Are you ready for some mathematical clowning around?
There are 500 numbers divisible by 2 (since every other number is divisible by 2), and there are 200 numbers divisible by 5 (as there are multiples of 5 up to 1000). But wait, we can't forget about those numbers that are divisible by both 2 and 5! These numbers are multiples of 10, which means they've already been counted as multiples of 2.
So, to find the total count of numbers divisible by either 2 or 5, we add the number of multiples of 2 (500) and the number of multiples of 5 (200), and then subtract the number of multiples of 10 (100). That gives us a grand total of 600 numbers.
Now, the probability of randomly picking a number divisible by either 2 or 5 out of the range 1 to 1000 is the number of desired outcomes (600) divided by the total number of possible outcomes (1000), which simplifies to 3/5 or 0.6.
So, the probability that the number you randomly pick is divisible by either 2 or 5 is 0.6, or 60%. Just remember, this calculation is strictly for amusement purposes!
To find the probability that a number between 1 and 1000 is divisible by either 2 or 5, we need to determine the count of numbers divisible by 2, divisible by 5, and divisible by both 2 and 5.
Step 1: Count of numbers divisible by 2:
There are 500 numbers divisible by 2 between 1 and 1000. (1000/2 = 500)
Step 2: Count of numbers divisible by 5:
There are 200 numbers divisible by 5 between 1 and 1000. (1000/5 = 200)
Step 3: Count of numbers divisible by both 2 and 5 (or divisible by 10):
There are 100 numbers divisible by 10 between 1 and 1000. (1000/10 = 100)
Step 4: Calculate the count of numbers divisible by either 2 or 5:
To find the count of numbers divisible by either 2 or 5, we need to add the counts from steps 1 and 2 and then subtract the count from step 3 (to avoid double counting):
Count of numbers divisible by either 2 or 5 = Count divisible by 2 + Count divisible by 5 - Count divisible by 10 = 500 + 200 - 100 = 600.
Step 5: Calculate the probability:
The total number of possible choices is 1000 (from 1 to 1000). Therefore, the probability that a randomly chosen number between 1 and 1000 is divisible by either 2 or 5 is:
Probability = (Count of numbers divisible by either 2 or 5) / (Total number of possible choices) = 600 / 1000 = 0.6.
So, the probability that a randomly chosen number between 1 and 1000 is divisible by either 2 or 5 is 0.6 or 60%.
To calculate the probability that a number selected randomly between 1 and 1000 is divisible by either 2 or 5, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
First, let's find the total number of possible outcomes. Since we are picking a number from 1 to 1000, there are 1000 possible outcomes.
Now, let's determine the total number of favorable outcomes. We need to count the numbers that are divisible by either 2 or 5.
Numbers divisible by 2:
To find the count of numbers divisible by 2, we can note that every second number is divisible by 2. So, we divide the total number of possibilities (1000) by 2: 1000 / 2 = 500.
Numbers divisible by 5:
To find the count of numbers divisible by 5, we divide the range (1000) by 5 and take the floor value since we are only considering whole numbers. So, the count of numbers divisible by 5 is 1000 / 5 = 200.
However, we need to subtract the numbers divisible by both 2 and 5 (numbers divisible by 10). To find the count of numbers divisible by 10, we divide the range (1000) by 10: 1000 / 10 = 100.
Now, let's calculate the total number of favorable outcomes. We add the count of numbers divisible by 2 (500) and the count of numbers divisible by 5 (200), and then subtract the count of numbers divisible by 10 (100). Therefore, the total number of favorable outcomes is 500 + 200 - 100 = 600.
Finally, calculating the probability is done by dividing the total number of favorable outcomes by the total number of possible outcomes: 600 / 1000 = 0.6.
So, the probability that a randomly chosen number from 1 to 1000 is divisible by either 2 or 5 is 0.6 or 60%.